{"id":836,"date":"2020-08-07T19:03:13","date_gmt":"2020-08-07T19:03:13","guid":{"rendered":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/use-the-rectangular-coordinate-system-2\/"},"modified":"2021-08-31T21:18:53","modified_gmt":"2021-08-31T21:18:53","slug":"use-the-rectangular-coordinate-system-2","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/businesstechnicalmath\/chapter\/use-the-rectangular-coordinate-system-2\/","title":{"raw":"3.1 Use the Rectangular Coordinate System","rendered":"3.1 Use the Rectangular Coordinate System"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section it is expected that you will be able to:\n<ul>\n \t<li>Plot points in a rectangular coordinate system<\/li>\n \t<li>Verify solutions to an equation in two variables<\/li>\n \t<li>Complete a table of solutions to a linear equation<\/li>\n \t<li>Find solutions to a linear equation in two variables<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Plot Points on a Rectangular Coordinate System<\/h1>\nJust like maps use a grid system to identify locations, a grid system is used in algebra to show a relationship between two variables in a <strong>rectangular coordinate system<\/strong>. The rectangular coordinate system is also called the <em data-effect=\"italics\">xy<\/em>-plane or the \u2018coordinate plane.\u2019\n\nThe horizontal number line is called the <em data-effect=\"italics\">x-axis<\/em>. The vertical number line is called the <em data-effect=\"italics\">y-axis.<\/em> The <em data-effect=\"italics\">x<\/em>-axis and the <em data-effect=\"italics\">y<\/em>-axis together form the rectangular coordinate system. These axes divide a plane into four regions, called <strong data-effect=\"bold\">quadrants<\/strong>. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise. See <a href=\"#CNX_ElemAlg_Figure_04_01_001\">(Figure 1)<\/a>.\n\n\u2018Quadrant\u2019 has the root \u2018quad,\u2019 which means \u2018four.\u2019\n\n[caption id=\"\" align=\"aligncenter\" width=\"342\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/08\/CNX_ElemAlg_Figure_04_01_001_img_new.jpg\" alt=\"Described in previous paragraphs. Top right quadrant labelled \u201cI\u201d, top left \u201cII\u201d, bottom left \u201cIII\u201d, and bottom right \u201cIV\u201d.\" width=\"342\" height=\"351\" data-media-type=\"image\/jpeg\"> Figure .1[\/caption]\n\nIn the <span class=\"no-emphasis\" data-type=\"term\">rectangular coordinate system<\/span>, every point is represented by an <em data-effect=\"italics\">ordered pair<\/em>. The first number in the ordered pair is the\u00a0<span data-type=\"term\"><strong><em data-effect=\"italics\">x<\/em>-coordinate<\/strong><\/span> of the point, and the second number is the <strong><em data-effect=\"italics\">y<\/em>-coordinate<\/strong> of the point.\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Ordered pair<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nAn ordered pair, \\(\\left(x,y\\right)\\),\u00a0 gives the coordinates of a point in a rectangular coordinate system.<span id=\"fs-id1169596440557\" data-type=\"media\" data-alt=\"The ordered pair x y is labeled with the first coordinate x labeled as &quot;x-coordinate&quot; and the second coordinate y labeled as &quot;y-coordinate&quot;.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_033_img_new.jpg\" alt=\"Ordered pair x y. The first coordinate x labeled &quot;x-coordinate&quot;, the second coordinate y labeled &quot;y-coordinate&quot;.\" width=\"250\" height=\"59\" data-media-type=\"image\/jpeg\"><\/span>\n<p style=\"text-align: left;\">The first number is the x-coordinate.<\/p>\n<p class=\"hanging-indent\">The second number is the y-coordinate.<\/p>\n\n<\/div>\n<\/div>\nThe phrase \u2018ordered pair\u2019 means the order is important. What is the ordered pair of the point where the axes cross? At that point both coordinates are zero, so its ordered pair is \\(\\left(0,0\\right)\\). The point \\(\\left(0,0\\right)\\) has a special name. It is called the <strong><span class=\"no-emphasis\" data-type=\"term\">origin<\/span><\/strong>.\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">The origin<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nThe point \\(\\left(0,0\\right)\\) is called the <span data-type=\"term\">origin<\/span>. It is the point where the <em data-effect=\"italics\">x<\/em>-axis and <em data-effect=\"italics\">y<\/em>-axis intersect.\n\n<\/div>\n<\/div>\nWe use the coordinates to locate a point on the <em data-effect=\"italics\">xy<\/em>-plane. Let\u2019s plot the point \\(\\left(1,3\\right)\\) as an example. First, locate 1 on the <em data-effect=\"italics\">x<\/em>-axis and lightly sketch a vertical line through \\(x=1\\). Then, locate 3 on the <em data-effect=\"italics\">y<\/em>-axis and sketch a horizontal line through \\(y=3\\). Now, find the point where these two lines meet\u2014that is the point with coordinates \\(\\left(1,3\\right)\\).\n\n[caption id=\"\" align=\"aligncenter\" width=\"301\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_002_img_new.jpg\" alt=\"Figure 2. The result of the process described in previous paragraph plotting the point (1,3).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"> Figure .2[\/caption]\n\nNotice that the vertical line through \\(x=1\\) and the horizontal line through \\(y=3\\) are not part of the graph. We just used them to help us locate the point \\(\\left(1,3\\right)\\).\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nPlot each point in the rectangular coordinate system and identify the <span class=\"no-emphasis\" data-type=\"term\">quadrant<\/span> in which the point is located:\n\n<span class=\"token\">A <\/span>\\(\\left(-5,4\\right)\\)\u2003<span class=\"token\">B <\/span>\\(\\left(-3,-4\\right)\\)\u2003<span class=\"token\">C <\/span>\\(\\left(2,-3\\right)\\)\u2003<span class=\"token\">D <\/span>\\(\\left(-2,3\\right)\\)\u2003<span class=\"token\">E <\/span>\\(\\left(3,\\frac{5}{2}\\right)\\).\n\n<strong>Solution\n<\/strong>\n\nThe first number of the coordinate pair is the <em data-effect=\"italics\">x<\/em>-coordinate, and the second number is the <em data-effect=\"italics\">y<\/em>-coordinate.\n<ol type=\"A\">\n \t<li>Since \\(x=-5\\), the point is to the left of the <em data-effect=\"italics\">y<\/em>-axis. Also, since \\(y=4\\), the point is above the <em data-effect=\"italics\">x<\/em>-axis. The point \\(\\left(-5,4\\right)\\) is in Quadrant II.<\/li>\n \t<li>Since \\(x=-3\\), the point is to the left of the <em data-effect=\"italics\">y<\/em>-axis. Also, since \\(y=-4\\), the point is below the <em data-effect=\"italics\">x<\/em>-axis. The point \\(\\left(-3,-4\\right)\\) is in Quadrant III.<\/li>\n \t<li>Since \\(x=2\\), the point is to the right of the <em data-effect=\"italics\">y<\/em>-axis. Since \\(y=-3\\), the point is below the <em data-effect=\"italics\">x<\/em>-axis. The point \\(\\left(2,-3\\right)\\) is in Quadrant lV.<\/li>\n \t<li>Since \\(x=-2\\), the point is to the left of the <em data-effect=\"italics\">y<\/em>-axis. Since \\(y=3\\), the point is above the <em data-effect=\"italics\">x<\/em>-axis. The point \\(\\left(-2,3\\right)\\) is in Quadrant II.<\/li>\n \t<li>Since \\(x=3\\), the point is to the right of the <em data-effect=\"italics\">y<\/em>-axis. Since \\(y=\\frac{5}{2}\\), the point is above the <em data-effect=\"italics\">x<\/em>-axis. (It may be helpful to write \\(\\frac{5}{2}\\) as a mixed number or decimal.) The point \\(\\left(3,\\frac{5}{2}\\right)\\) is in Quadrant I.<span data-type=\"newline\">\n<\/span><\/li>\n<\/ol>\n<p id=\"CNX_ElemAlg_Figure_04_01_003\" class=\"bc-figure figure indent hanging-indent\"><span id=\"fs-id1169596298887\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 5, 4), (negative 2, 3), (negative 3, negative 4), (3, five halves), and (2, negative 3) are plotted and labeled.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_003_img_new.jpg\" alt=\"A graph plotting the points (-5, 4), (-2, 3), (-3, -4), (3, 5\/2), and (2, -3).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span><\/p>\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nPlot each point in a rectangular coordinate system and identify the quadrant in which the point is located:\n\n<span class=\"token\">A <\/span>\\(\\left(-2,1\\right)\\)\u2003<span class=\"token\">B <\/span>\\(\\left(-3,-1\\right)\\)\u2003<span class=\"token\">C <\/span>\\(\\left(4,-4\\right)\\)\u2003<span class=\"token\">D <\/span>\\(\\left(-4,4\\right)\\)\u2003<span class=\"token\">E <\/span>\\(\\left(-4,\\frac{3}{2}\\right)\\).\n\n<details><summary class=\"answer\">Show answer<\/summary><span id=\"fs-id1169596376606\" data-type=\"solution\"><span id=\"fs-id1169594008202\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 2, 1) is plotted and labeled &quot;a&quot;. The point (negative 3, negative 1) is plotted and labeled &quot;b&quot;. The point (4, negative 4) is plotted and labeled &quot;c&quot;. The point (negative 4, negative one half) is plotted and labeled \u201cd\u201d.\"><span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_026_img_new.jpg\" alt=\"A graph plotting the points described in the previous paragraph.\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\"><\/span><\/span>\n\n<\/details><\/div>\n<\/div>\nHow do the signs affect the location of the points? You may have noticed some patterns as you graphed the points in the previous example.\n\nFor the point in <a class=\"autogenerated-content\" href=\"#fs-id1169596587993\">(Figure 2)<\/a> in Quadrant IV, what do you notice about the signs of the coordinates? What about the signs of the coordinates of points in the third quadrant? The second quadrant? The first quadrant?\n\nCan you tell just by looking at the coordinates in which quadrant the point \\(\\left(-2,5\\right)\\) is located? In which quadrant is \\(\\left(2,-5\\right)\\) located?\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Quadrants<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nWe can summarize sign patterns of the quadrants in this way.\\(\\begin{array}{cccc}\\hfill \\text{Quadrant I}\\hfill &amp;\\hfill \\text{Quadrant II}\\hfill &amp;\u00a0 \\hfill \\text{Quadrant III}\\hfill &amp; \\hfill \\text{Quadrant IV}\\hfill \\\\ \\hfill \\left(x,y\\right)\\hfill &amp; \\hfill \\left(x,y\\right)\\hfill &amp;\u00a0 \\hfill \\left(x,y\\right)\\hfill &amp; \\hfill \\left(x,y\\right)\\hfill \\\\ \\hfill \\left(+,+\\right)\\hfill &amp;\u00a0 \\hfill \\left(\\text{\u2212},+\\right)\\hfill &amp; \\hfill \\left(\\text{\u2212},\\text{\u2212}\\right)\\hfill &amp;\u00a0 \\hfill \\left(+,\\text{\u2212}\\right)\\hfill \\end{array}\\)\n\n<span id=\"fs-id1169596767978\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The top-right portion of the plane is labeled &quot;I&quot; and &quot;ordered pair +, +&quot;, the top-left portion of the plane is labeled &quot;II&quot; and &quot;ordered pair -, +&quot;, the bottom-left portion of the plane is labelled &quot;III&quot; &quot;ordered pair -, -&quot; and the bottom-right portion of the plane is labeled &quot;IV&quot; and &quot;ordered pair +, -&quot;.\"><span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\"><span id=\"fs-id1169596298887\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 5, 4), (negative 2, 3), (negative 3, negative 4), (3, five halves), and (2, negative 3) are plotted and labeled.\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> <\/span><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_004_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The top-right portion of the plane is labeled &quot;I&quot; and &quot;ordered pair +, +&quot;, the top-left portion of the plane is labeled &quot;II&quot; and &quot;ordered pair -, +&quot;, the bottom-left portion of the plane is labelled &quot;III&quot; &quot;ordered pair -, -&quot; and the bottom-right portion of the plane is labeled &quot;IV&quot; and &quot;ordered pair +, -&quot;.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\nWhat if one coordinate is zero as shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_01_005\">(Figure 3)<\/a>? Where is the point \\(\\left(0,4\\right)\\) located? Where is the point \\(\\left(-2,0\\right)\\) located?<span data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. Points (0, 4) and (negative 2, 0) are plotted and labeled.\"><span data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. Points (0, 4) and (negative 2, 0) are plotted and labeled.\"><span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\"><span id=\"fs-id1169596298887\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 5, 4), (negative 2, 3), (negative 3, negative 4), (3, five halves), and (2, negative 3) are plotted and labeled.\"> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> <\/span><\/span><\/span>\n\n[caption id=\"\" align=\"aligncenter\" width=\"301\"]<img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_005_img_new.jpg\" alt=\" A graph plotting the points (0, 4) and (negative 2, 0).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"> Figure .3<span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\"> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span>[\/caption]\n\nThe point \\(\\left(0,4\\right)\\) is on the <em data-effect=\"italics\">y<\/em>-axis and the point \\(\\left(-2,0\\right)\\) is on the <em data-effect=\"italics\">x<\/em>-axis.\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Points on the axes<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nPoints with a <span class=\"no-emphasis\" data-type=\"term\"><em data-effect=\"italics\">y<\/em>-coordinate<\/span> equal to 0 are on the <em data-effect=\"italics\">x<\/em>-axis, and have coordinates \\(\\left(a,0\\right)\\).\n\nPoints with an <span class=\"no-emphasis\" data-type=\"term\"><em data-effect=\"italics\">x<\/em>-coordinate<\/span> equal to 0 are on the <em data-effect=\"italics\">y<\/em>-axis, and have coordinates \\(\\left(0,b\\right)\\).\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nPlot each point:<span class=\"token\">A <\/span>\\(\\left(0,5\\right)\\)\u2003<span class=\"token\">B <\/span>\\(\\left(4,0\\right)\\)\u2003<span class=\"token\">C <\/span>\\(\\left(-3,0\\right)\\)\u2003<span class=\"token\">D <\/span>\\(\\left(0,0\\right)\\)\u2003<span class=\"token\">E <\/span>\\(\\left(0,-1\\right)\\).\n\n<strong>Solution<\/strong>\n<ol id=\"fs-id1169597525788\" class=\"circled\" type=\"A\">\n \t<li>Since \\(x=0\\), the point whose coordinates are \\(\\left(0,5\\right)\\) is on the <em data-effect=\"italics\">y<\/em>-axis.<\/li>\n \t<li>Since \\(y=0\\), the point whose coordinates are \\(\\left(4,0\\right)\\) is on the <em data-effect=\"italics\">x<\/em>-axis.<\/li>\n \t<li>Since \\(y=0\\), the point whose coordinates are \\(\\left(-3,0\\right)\\) is on the <em data-effect=\"italics\">x<\/em>-axis.<\/li>\n \t<li>Since \\(x=0\\) and \\(y=0\\), the point whose coordinates are \\(\\left(0,0\\right)\\) is the origin.<\/li>\n \t<li>Since \\(x=0\\), the point whose coordinates are \\(\\left(0,-1\\right)\\) is on the <em data-effect=\"italics\">y<\/em>-axis.<span data-type=\"newline\">\n<\/span><span id=\"fs-id1169596653858\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 3, 0), (0, 0), (0, negative 1), (0, 5), and (4, 0) are plotted and labeled.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_006_img_new.jpg\" alt=\"A graph plotting the points (negative 3, 0), (0, 0), (0, negative 1), (0, 5), and (4, 0).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nPlot each point:<span class=\"token\">A <\/span>\\(\\left(4,0\\right)\\)\u2003<span class=\"token\">B <\/span>\\(\\left(-2,0\\right)\\)\u2003<span class=\"token\">C <\/span>\\(\\left(0,0\\right)\\)\u2003<span class=\"token\">D <\/span>\\(\\left(0,2\\right)\\)\u2003<span class=\"token\">E <\/span>\\(\\left(0,-3\\right)\\).\n\n<details><summary class=\"answer\">Show answer<\/summary><span id=\"fs-id1169596654134\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled.\"><span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span> <img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_028_img_new.jpg\" alt=\"A graph plotting the points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3).\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/details><\/div>\n<\/div>\nIn algebra, being able to identify the coordinates of a point shown on a graph is just as important as being able to plot points. To identify the <em data-effect=\"italics\">x<\/em>-coordinate of a point on a graph, read the number on the <em data-effect=\"italics\">x<\/em>-axis directly above or below the point. To identify the <em data-effect=\"italics\">y<\/em>-coordinate of a point, read the number on the <em data-effect=\"italics\">y<\/em>-axis directly to the left or right of the point. Remember, when you write the <span class=\"no-emphasis\" data-type=\"term\">ordered pair<\/span> use the correct order, \\(\\left(x,y\\right)\\).\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nName the ordered pair of each point shown in the rectangular coordinate system.<span id=\"fs-id1169596453833\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled A, B, C, D, and E, respectively.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_007_img_new.jpg\" alt=\"Described in following paragraph.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span>\n\n<strong>Solution<\/strong>\n\nPoint A is above \\(-3\\) on the <em data-effect=\"italics\">x<\/em>-axis, so the <em data-effect=\"italics\">x<\/em>-coordinate of the point is \\(-3\\).\n<ul id=\"fs-id1169594050927\" data-bullet-style=\"bullet\">\n \t<li>The point is to the left of 3 on the <em data-effect=\"italics\">y<\/em>-axis, so the <em data-effect=\"italics\">y<\/em>-coordinate of the point is 3.<\/li>\n \t<li>The coordinates of the point are \\(\\left(-3,3\\right)\\).<\/li>\n<\/ul>\n<p id=\"fs-id1169594155473\">Point B is below \\(-1\\) on the <em data-effect=\"italics\">x<\/em>-axis, so the <em data-effect=\"italics\">x<\/em>-coordinate of the point is \\(-1\\).<\/p>\n\n<ul id=\"fs-id1169594029277\" data-bullet-style=\"bullet\">\n \t<li>The point is to the left of \\(-3\\) on the <em data-effect=\"italics\">y<\/em>-axis, so the <em data-effect=\"italics\">y<\/em>-coordinate of the point is \\(-3\\).<\/li>\n \t<li>The coordinates of the point are \\(\\left(-1,-3\\right)\\).<\/li>\n<\/ul>\n<p id=\"fs-id1169596555335\">Point C is above 2 on the <em data-effect=\"italics\">x<\/em>-axis, so the <em data-effect=\"italics\">x<\/em>-coordinate of the point is 2.<\/p>\n\n<ul id=\"fs-id1169596282410\" data-bullet-style=\"bullet\">\n \t<li>The point is to the right of 4 on the <em data-effect=\"italics\">y<\/em>-axis, so the <em data-effect=\"italics\">y<\/em>-coordinate of the point is 4.<\/li>\n \t<li>The coordinates of the point are \\(\\left(2,4\\right)\\).<\/li>\n<\/ul>\n<p id=\"fs-id1169594159149\">Point D is below 4 on the <em data-effect=\"italics\">x<\/em>-axis, so the <em data-effect=\"italics\">x<\/em>-coordinate of the point is 4.<\/p>\n\n<ul id=\"fs-id1169594078395\" data-bullet-style=\"bullet\">\n \t<li>The point is to the right of \\(-4\\) on the <em data-effect=\"italics\">y<\/em>-axis, so the <em data-effect=\"italics\">y<\/em>-coordinate of the point is \\(-4.\\)<\/li>\n \t<li>The coordinates of the point are \\(\\left(4,-4\\right)\\).<\/li>\n<\/ul>\n<p id=\"fs-id1169596393241\">Point E is on the <em data-effect=\"italics\">y<\/em>-axis at \\(y=-2\\). The coordinates of point E are \\(\\left(0,-2\\right).\\)<\/p>\n<p id=\"fs-id1169594050420\">Point F is on the <em data-effect=\"italics\">x<\/em>-axis at \\(x=3\\). The coordinates of point F are \\(\\left(3,0\\right).\\)<\/p>\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nName the ordered pair of each point shown in the rectangular coordinate system.<span id=\"fs-id1169594087555\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled A, B, C, D, and E, respectively.\"><span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\"><span id=\"fs-id1169596453833\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled A, B, C, D, and E, respectively.\"><span id=\"fs-id1169596653858\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 3, 0), (0, 0), (0, negative 1), (0, 5), and (4, 0) are plotted and labeled.\"><span id=\"fs-id1169596298887\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 5, 4), (negative 2, 3), (negative 3, negative 4), (3, five halves), and (2, negative 3) are plotted and labeled.\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/span><\/span> <\/span><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_030_img_new.jpg\" alt=\"A graph plotting the points (5, 1), (negative 2, 4), (negative 5, negative 1), (3, negative 2), (0, negative 5) labelled A-E.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span>\n\n<details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596446575\">A: \\(\\left(5,1\\right)\\)\u2003B: \\(\\left(-2,4\\right)\\)\u2003C: \\(\\left(-5,-1\\right)\\)\u2003D: \\(\\left(3,-2\\right)\\)\u2003E: \\(\\left(0,-5\\right)\\)\u2003F: \\(\\left(4,0\\right)\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<h1>Verify Solutions to an Equation in Two Variables<\/h1>\nUp to now, all the equations you have solved were equations with just one variable. In almost every case, when you solved the equation you got exactly one solution. The process of solving an equation ended with a statement like \\(x=4\\). (Then, you checked the solution by substituting back into the equation.)\nHere\u2019s an example of an equation in one variable, and its one solution.\n\n\\(\\begin{array}{ccc}\\hfill 3x+5&amp; =\\hfill &amp; 17\\hfill \\\\ \\hfill 3x&amp; =\\hfill &amp; 12\\hfill \\\\ \\hfill x&amp; =\\hfill &amp; 4\\hfill \\end{array}\\)\n\nBut equations can have more than one variable. Equations with two variables may be of the form \\(Ax+By=C\\). Equations of this form are called <strong data-effect=\"bold\">linear equations in two variables<\/strong>.\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Linear equation<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nAn equation of the form \\(Ax+By=C\\), where \\(A\\) and \\(B\\) are not both zero, is called a <span data-type=\"term\">linear equation<\/span> <strong data-effect=\"bold\">in two variables<\/strong>.\n\n<\/div>\n<\/div>\nNotice the word <em data-effect=\"italics\">line<\/em> in <strong data-effect=\"bold\">linear<\/strong>. Here is an example of a linear equation in two variables, \\(x\\) and \\(y\\).\n\n<span id=\"fs-id1169596652462\" data-type=\"media\" data-alt=\"In this figure, we see the linear equation Ax plus By equals C. Below this is the equation x plus 4y equals 8. Below this are the values A equals 1, B equals 4, and C equals 8.\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_032_img_new.jpg\" alt=\"In this figure, we see the linear equation Ax plus By equals C. Below this is the equation x plus 4y equals 8. Below this are the values A equals 1, B equals 4, and C equals 8.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169596240065\">The equation \\(y=-3x+5\\) is also a <span class=\"no-emphasis\" data-type=\"term\">linear equation<\/span>. But it does not appear to be in the form \\(Ax+By=C\\). We can use the Addition Property of Equality and rewrite it in \\(Ax+By=C\\) form.<\/p>\n\n<table id=\"eip-439\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(y=-3x+5\\)<\/td>\n<\/tr>\n<tr>\n<td>Add to both sides.<\/td>\n<td>\\(y+3x=-3x+5+3x\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(y+3x=5\\)<\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to put it in \\(Ax+By=C\\) form.<\/td>\n<td>\\(3x+y=5\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594031828\">By rewriting \\(y=-3x+5\\) as \\(3x+y=5\\), we can easily see that it is a linear equation in two variables because it is of the form \\(Ax+By=C\\). When an equation is in the form \\(Ax+By=C\\), we say it is in <em data-effect=\"italics\">standard form<\/em>.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Standard Form of Linear Equation<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nA linear equation is in standard form when it is written \\(Ax+By=C\\).\n\n<\/div>\n<\/div>\nMost people prefer to have \\(A\\), \\(B\\), and \\(C\\) be integers and \\(A\\ge 0\\) when writing a linear equation in standard form, although it is not strictly necessary.\n\nLinear equations have infinitely many solutions. For every number that is substituted for \\(x\\) there is a corresponding \\(y\\) value. This pair of values is a <em data-effect=\"italics\">solution<\/em> to the linear equation and is represented by the ordered pair \\(\\left(x,y\\right)\\). When we substitute these values of \\(x\\) and \\(y\\) into the equation, the result is a true statement, because the value on the left side is equal to the value on the right side.\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Solution of a Linear Equation in Two Variables<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nAn <span data-type=\"term\">ordered pair<\/span> \\(\\left(x,y\\right)\\) is a <strong data-effect=\"bold\">solution<\/strong> of the linear equation \\(Ax+By=C\\), if the equation is a true statement when the <em data-effect=\"italics\">x<\/em>- and <em data-effect=\"italics\">y<\/em>-values of the ordered pair are substituted into the equation.\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nDetermine which ordered pairs are solutions to the equation \\(x+4y=8\\).\n\nA (\\left(0,2\\right)\\)\u2003B \\(\\left(2,-4\\right)\\)\u2003C \\(\\left(-4,3\\right)\\)\n\n<strong>Solution<\/strong>\n\nSubstitute the x- and y-values from each ordered pair into the equation and determine if the result is a true statement.\n\n<img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_034_img_new.jpg\" alt=\"This figure has three columns. At the top of the first column is the ordered pair (0, 2). Below this are the values x equals 0 and y equals 2. Below this is the equation x plus 4y equals 8. Below this is the same equation with 0 and 2 substituted for x and y: 0 plus 4 times 2 might equal 8. Below this is 0 plus 8 might equal 8. Below this is 8 equals 8 with a check mark next to it. Below this is the sentence \u201c(0, 2) is a solution.\u201d At the top of the second column is the ordered pair (2, negative 4). Below this are the values x equals 2 and y equals negative 4. Below this is the equation x plus 4y equals 8. Below this is the same equation with 2 and negative 4 substituted for x and y: 2 plus 4 times negative 4 might equal 8. Below this is 2 plus negative 16 might equal 8. Below this is negative 14 does not equal 8. Below this is the sentence: \u201c(2, negative 4) is not a solution.\u201d At the top of the third column is the ordered pair (negative 4, 3). Below this are the values x equals negative 4 and y equals 3. Below this is the equation x plus 4y equals 8. Below this is the same equation with negative 4 and 3 substituted for x and y: negative 4 plus 4 times 3 might equal 8. Below this is negative 4 plus 12 might equal 8. Below this is 8 equals 8 with a check mark next to it. Below this is the sentence: \u201c(negative 4, 3) is a solution.\u201d\" data-media-type=\"image\/jpeg\">\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nWhich of the following ordered pairs are solutions to \\(2x+3y=6\\)?\n<span class=\"token\">A <\/span>\\(\\left(3,0\\right)\\)\u2003<span class=\"token\">B <\/span>\\(\\left(2,0\\right)\\)\u2003<span class=\"token\">C <\/span>\\(\\left(6,-2\\right)\\)\n\n<details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596655873\">A, C<\/p>\n\n<\/details><\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nWhich of the following ordered pairs are solutions to the equation \\(y=5x-1\\)?\n\n<span class=\"token\">A <\/span>\\(\\left(0,-1\\right)\\)\u2003<span class=\"token\">B <\/span>\\(\\left(1,4\\right)\\)\u2003<span class=\"token\">C <\/span>\\(\\left(-2,-7\\right)\\)\n\n<strong>Solution<\/strong>\n\nSubstitute the <em data-effect=\"italics\">x<\/em>- and <em data-effect=\"italics\">y<\/em>-values from each <span class=\"no-emphasis\" data-type=\"term\">ordered pair<\/span> into the equation and determine if it results in a true statement.<span data-type=\"newline\">\n<\/span>\n\n<span id=\"fs-id1169596658144\" data-type=\"media\" data-alt=\"This figure has three columns. At the top of the first column is the ordered pair (0, negative 1). Below this are the values x equals 0 and y equals negative 1. Below this is the equation y equals 5x minus 1. Below this is the same equation with 0 and negative 1 substituted for x and y: negative 1 might equal 5 times 0 minus 1. Below this is negative 1 might equal 0 minus 1. Below this is negative 1 equals negative 1 with a check mark next to it. Below this is the sentence: \u201c(0, negative 1) is a solution.\u201d At the top of the second column is the ordered pair (1, 4). Below this are the values x equals 1 and y equals 4. Below this is the equation y equals 5x minus 1. Below this is the same equation with 1 and 4 substituted for x and y: 4 might equal 5 times 1 minus 1. Below this is 4 might equal 5 minus 1. Below this is 4 equals 4 with a check mark next to it. Below this is the sentence: \u201c(1, 4) is a solution.\u201d At the top of the right column is the ordered pair (negative 2, negative 7). Below this are the values x equals negative 2 and y equals negative 7. Below this is the equation y equals 5x minus 1. Below this is the same equation with negative 2 and negative 7 substituted for x and y: negative 7 might equal 5 times negative 2 minus 1. Below this is negative 7 might equal negative 10 minus 1. Below this is negative 7 does not equal negative 11. Below this is the sentence: \u201c(negative 2, negative 7) is not a solution.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_035_img_new.jpg\" alt=\"This figure has three columns. At the top of the first column is the ordered pair (0, negative 1). Below this are the values x equals 0 and y equals negative 1. Below this is the equation y equals 5x minus 1. Below this is the same equation with 0 and negative 1 substituted for x and y: negative 1 might equal 5 times 0 minus 1. Below this is negative 1 might equal 0 minus 1. Below this is negative 1 equals negative 1 with a check mark next to it. Below this is the sentence: \u201c(0, negative 1) is a solution.\u201d At the top of the second column is the ordered pair (1, 4). Below this are the values x equals 1 and y equals 4. Below this is the equation y equals 5x minus 1. Below this is the same equation with 1 and 4 substituted for x and y: 4 might equal 5 times 1 minus 1. Below this is 4 might equal 5 minus 1. Below this is 4 equals 4 with a check mark next to it. Below this is the sentence: \u201c(1, 4) is a solution.\u201d At the top of the right column is the ordered pair (negative 2, negative 7). Below this are the values x equals negative 2 and y equals negative 7. Below this is the equation y equals 5x minus 1. Below this is the same equation with negative 2 and negative 7 substituted for x and y: negative 7 might equal 5 times negative 2 minus 1. Below this is negative 7 might equal negative 10 minus 1. Below this is negative 7 does not equal negative 11. Below this is the sentence: \u201c(negative 2, negative 7) is not a solution.\u201d\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nWhich of the following ordered pairs are solutions to the equation \\(y=4x-3\\)? <span class=\"token\">A <\/span>\\(\\left(0,3\\right)\\)\u2003<span class=\"token\">B <\/span>\\(\\left(1,1\\right)\\)\u2003<span class=\"token\">C <\/span>\\(\\left(-1,-1\\right)\\)\n\n<details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596658490\">B<\/p>\n\n<\/details><\/div>\n<\/div>\n<h1>Complete a Table of Solutions to a Linear Equation in Two Variables<\/h1>\n<p id=\"fs-id1169596684664\">In the examples above, we substituted the <em data-effect=\"italics\">x<\/em>- and <em data-effect=\"italics\">y<\/em>-values of a given ordered pair to determine whether or not it was a solution to a linear equation. But how do you find the ordered pairs if they are not given? It\u2019s easier than you might think\u2014you can just pick a value for \\(x\\) and then solve the equation for \\(y\\). Or, pick a value for \\(y\\) and then solve for \\(x\\).<\/p>\n<p id=\"fs-id1169596243344\">We\u2019ll start by looking at the solutions to the equation \\(y=5x-1\\) that we found in <a class=\"autogenerated-content\" href=\"#fs-id1169596400539\">(Example 5)<\/a>. We can summarize this information in a table of solutions, as shown in <a class=\"autogenerated-content\" href=\"#fs-id1169594029160\">(Table 1)<\/a>.<\/p>\n\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"height: 64px; width: 457px;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\">\\(y=5x-1\\)<\/strong><\/span><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 75.7344px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/span><\/td>\n<td style=\"width: 83.8125px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/span><\/td>\n<td style=\"width: 249.172px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 75.7344px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">0<\/span><\/td>\n<td style=\"width: 83.8125px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">\\(-1\\)<\/span><\/td>\n<td style=\"width: 249.172px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">\\(\\left(0,-1\\right)\\)<\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 75.7344px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">1<\/span><\/td>\n<td style=\"width: 83.8125px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">4<\/span><\/td>\n<td style=\"width: 249.172px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">\\(\\left(1,4\\right)\\)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596685318\">To find a third solution, we\u2019ll let \\(x=2\\) and solve for \\(y\\).<\/p>\n<span id=\"fs-id1169596685335\" data-type=\"media\" data-alt=\"The figure shows the steps to solve for y when x equals 2 in the equation y equals 5 x minus 1. The equation y equals 5 x minus 1 is shown. Below it is the equation with 2 substituted in for x which is y equals 5 times 2 minus 1. To solve for y first multiply so that the equation becomes y equals 10 minus 1 then subtract so that the equation is y equals 9.\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_040_img_new.jpg\" alt=\"The figure shows the steps to solve for y when x equals 2 in the equation y equals 5 x minus 1. The equation y equals 5 x minus 1 is shown. Below it is the equation with 2 substituted in for x which is y equals 5 times 2 minus 1. To solve for y first multiply so that the equation becomes y equals 10 minus 1 then subtract so that the equation is y equals 9.\" width=\"242\" height=\"112\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594160564\">The ordered pair \\(\\left(2,9\\right)\\) is a solution to \\(y=5x-1\\). We will add it to <a class=\"autogenerated-content\" href=\"#fs-id1169594160564\">(Table 2)<\/a>.<\/p>\n\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 406px;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\">\\(y=5x-1\\)<\/strong><\/span><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 76.3438px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/span><\/td>\n<td style=\"width: 84.375px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/span><\/td>\n<td style=\"width: 248px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 76.3438px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">0<\/span><\/td>\n<td style=\"width: 84.375px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">\\(-1\\)<\/span><\/td>\n<td style=\"width: 248px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">\\(\\left(0,-1\\right)\\)<\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 76.3438px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">1<\/span><\/td>\n<td style=\"width: 84.375px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">4<\/span><\/td>\n<td style=\"width: 248px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">\\(\\left(1,4\\right)\\)<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 76.3438px; text-align: center;\"><span style=\"background-color: #ffffff; color: #000000;\">2<\/span><\/td>\n<td style=\"width: 84.375px; text-align: center;\"><span style=\"background-color: #ffffff; color: #000000;\">9<\/span><\/td>\n<td style=\"width: 248px; text-align: center;\"><span style=\"background-color: #ffffff; color: #000000;\">\\(\\left(2,9\\right)\\)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596435756\">We can find more solutions to the equation by substituting in any value of \\(x\\) or any value of \\(y\\) and solving the resulting equation to get another ordered pair that is a solution. There are infinitely many solutions of this equation.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596437443\" style=\"text-align: center;\" data-type=\"problem\">\n<p id=\"fs-id1169596437445\">Complete the table\u00a0to find three solutions to the equation \\(y=4x-2\\).<\/p>\n\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 406px;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption>\\(y=4x-2\\)<\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">2<\/td>\n<td style=\"width: 81.4062px; text-align: center;\"><\/td>\n<td style=\"width: 240.406px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n&nbsp;\n\n<\/div>\n<div id=\"fs-id1169596388103\" style=\"text-align: center;\" data-type=\"solution\">\n<div style=\"text-align: left;\" data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596253289\">Substitute \\(x=0\\), \\(x=-1\\), and \\(x=2\\) into \\(y=4x-2\\).<span data-type=\"newline\">\n<\/span><\/p>\n<img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_036_img_new.jpg\" alt=\"This figure has three columns. At the top of the first column is the value x equals 0. Below this is the equation y equals 4x minus 2. Below this is the same equation with 0 substituted for x: y equals 4 times 0 minus 2. Below this is y equals 0 minus 2. Below this is y equals negative 2. Below this is the ordered pair (0, negative 2). At the top of the second column is the value x equals negative 1. Below this is the equation y equals 4x minus 2. Below this is the same equation with negative 1 substituted for x: y equals 4 times minus 1 minus 2. Below this is y equals negative 4 minus 2. Below this is y equals negative 6. Below this is the ordered pair (negative 1, negative 6). At the top of the third column is the value x equals 2. Below this is the equation y equals 4x minus 2. Below this is the same equation with 2 substituted for x: y equals 4 times 2 minus 2. Below this is y equals 8 minus 2. Below this is y equals 6. Below this is the ordered pair (2, 6).\" data-media-type=\"image\/jpeg\">\n<p id=\"fs-id1169594087041\">The results are summarized in the table below.<\/p>\n\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><strong data-effect=\"bold\">\\(y=4x-2\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-2\\)<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(0,-2\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-6\\)<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(-1,-6\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">2<\/td>\n<td style=\"width: 81.4062px; text-align: center;\">\u00a0 6<\/td>\n<td style=\"width: 240.406px; text-align: center;\">\\(\\left(2,6\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596764393\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596764397\" data-type=\"exercise\">\n<div id=\"fs-id1169596764399\" data-type=\"problem\">\n<p id=\"fs-id1169596764401\">Complete the table to find three solutions to this equation: \\(y=3x-1\\).<\/p>\n\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><strong data-effect=\"bold\">\\(y=3x-1\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">2<\/td>\n<td style=\"width: 81.4062px; text-align: center;\"><\/td>\n<td style=\"width: 240.406px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<details><summary class=\"answer\">Show answer<\/summary>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><strong data-effect=\"bold\">\\(y=3x-1\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(0,-1\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-4\\)<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(-1,-4\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">2<\/td>\n<td style=\"width: 81.4062px; text-align: center;\">5<\/td>\n<td style=\"width: 240.406px; text-align: center;\">\\(\\left(2,5\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594211909\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594211913\" data-type=\"exercise\">\n<div id=\"fs-id1169594105663\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596253005\" data-type=\"problem\">\n<p id=\"fs-id1169596253007\">Complete the table to find three solutions to the equation \\(5x-4y=20\\).<\/p>\n\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><strong data-effect=\"bold\">\\(5x-4y=20\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\"><\/td>\n<td style=\"width: 81.4062px; text-align: center;\">5<\/td>\n<td style=\"width: 240.406px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1169596421536\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169594243050\">Substitute the given value into the equation \\(5x-4y=20\\) and solve for the other variable. Then, fill in the values in the table.<span data-type=\"newline\">\n<\/span><\/p>\n<span id=\"fs-id1169594243073\" data-type=\"media\" data-alt=\"This figure has three columns. At the top of the first column is the value x equals 0. Below this is the equation 5x minus 4y equals 20. Below this is the same equation with 0 substituted for x: 5 times 0 minus 4y equals 20. Below this is 0 minus 4y equals 20. Below this is negative 4y equals 20. Below this is y equals negative 5. Below this is the ordered pair (0, negative 5). At the top of the second column is the value y equals 0. Below this is the equation 5x minus 4y equals 20. Below this is the same equation with 0 substituted for y: 5x minus 4 times 0 equals 20. Below this is 5x minus 0 equals 20. Below this is 5x equals 20. Below this is x equals 4. Below this is the ordered pair (4, 0). At the top of the third column is the value y equals 5. Below this is the equation 5x minus 47 equals 20. Below this is the same equation with 5 substituted for y: 5x minus 4 times 5 equals 20. Below this is the equation 5x minus 20 equals 20. Below this is 5x equals 40. Below this is x equals 8. Below this is the ordered pair (8, 5).\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_037_img_new.jpg\" alt=\"This figure has three columns. At the top of the first column is the value x equals 0. Below this is the equation 5x minus 4y equals 20. Below this is the same equation with 0 substituted for x: 5 times 0 minus 4y equals 20. Below this is 0 minus 4y equals 20. Below this is negative 4y equals 20. Below this is y equals negative 5. Below this is the ordered pair (0, negative 5). At the top of the second column is the value y equals 0. Below this is the equation 5x minus 4y equals 20. Below this is the same equation with 0 substituted for y: 5x minus 4 times 0 equals 20. Below this is 5x minus 0 equals 20. Below this is 5x equals 20. Below this is x equals 4. Below this is the ordered pair (4, 0). At the top of the third column is the value y equals 5. Below this is the equation 5x minus 47 equals 20. Below this is the same equation with 5 substituted for y: 5x minus 4 times 5 equals 20. Below this is the equation 5x minus 20 equals 20. Below this is 5x equals 40. Below this is x equals 8. Below this is the ordered pair (8, 5).\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1169594243093\">The results are summarized in the table below.<\/p>\n\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><strong data-effect=\"bold\">\\(5x-4y=20\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.2812px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 81.2969px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 240.844px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.2812px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.2969px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-5\\)<\/td>\n<td style=\"width: 240.844px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(0,-5\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.2812px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td style=\"width: 81.2969px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 240.844px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(4,0\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.2812px; text-align: center;\">8<\/td>\n<td style=\"width: 81.2969px; text-align: center;\">5<\/td>\n<td style=\"width: 240.844px; text-align: center;\">\\(\\left(8,5\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596684659\" class=\"bc-section section\" data-depth=\"1\">\n<div id=\"fs-id1169596243950\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596243954\" data-type=\"exercise\">\n<div id=\"fs-id1169596243956\" data-type=\"problem\">\n<p id=\"fs-id1169596243958\">Complete the table to find three solutions to this equation: \\(2x-5y=20\\).<\/p>\n\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><strong data-effect=\"bold\">\\(2x-5y=20\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">\\(-5\\)<\/td>\n<td style=\"width: 81.4062px; text-align: center;\"><\/td>\n<td style=\"width: 240.406px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1169596446946\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><strong data-effect=\"bold\">\\(2x-5y=20\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-4\\)<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(0,-4\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">10<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(10,0\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">\\(-5\\)<\/td>\n<td style=\"width: 81.4062px; text-align: center;\">\\(-6\\)<\/td>\n<td style=\"width: 240.406px; text-align: center;\">\\(\\left(-5,-6\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find Solutions to a Linear Equation<\/h1>\n<p id=\"fs-id1169594031699\">To find a solution to a linear equation, you really can pick <em data-effect=\"italics\">any<\/em> number you want to substitute into the equation for \\(x\\) or \\(y.\\) But since you\u2019ll need to use that number to solve for the other variable it\u2019s a good idea to choose a number that\u2019s easy to work with.<\/p>\n<p id=\"fs-id1169596368122\">When the equation is in <em data-effect=\"italics\">y<\/em>-form, with the <em data-effect=\"italics\">y<\/em> by itself on one side of the equation, it is usually easier to choose values of \\(x\\) and then solve for \\(y\\).<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nFind three solutions to the equation \\(y=-3x+2\\).\n<div id=\"fs-id1169596368171\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596439896\">We can substitute any value we want for \\(x\\) or any value for \\(y\\). Since the equation is in <em data-effect=\"italics\">y<\/em>-form, it will be easier to substitute in values of \\(x\\). Let\u2019s pick \\(x=0\\), \\(x=1\\), and \\(x=-1\\).<span data-type=\"newline\">\n<\/span><\/p>\n\n<table id=\"eip-id1172184886219\" style=\"height: 172px; width: 100%;\" summary=\"This figure contains three columns. The leftmost column contains step-by-step instructions for finding ordered pairs that are solutions to the equation y equals negative 3x plus 2. These steps are: \u201cSubstitute the value into the equation,\u201d \u201cSimplify\u201d, \u201cSolve,\u201d \u201cWrite the ordered pair,\u201d and \u201cCheck.\u201d At the top of the second column is the value x equals 0. Below this is the equation y equals negative 3x plus 2. Below this is the equation with 0 substituted for x: y equals negative 3 times 0 plus 2. Below this is the equation simplified: y equals 0 plus 2. Below this is the equation solved: y equals 2. Below this is the ordered pair (0, 2). Below this is the equation y equals negative 3x plus 2 again. Below this is the equation with 0 and 2 substituted for x and y, ready to be checked: 2 might equal negative 3 times 0 plus 2. Below this is 2 might equal 0 plus 2. Below this is 2 equals 2, with a check mark next to it. At the top of the third column is the value x equals 1. Below this is the equation y equals negative 3x plus 2. Below this is the equation with 1 substituted for x: y equals negative 3 times 1 plus 2. Below this is the equation simplified: y equals negative 3 plus 2. Below this is the equation solved: y equals negative 1. Below this is the ordered pair (1, negative 1). Below this is the equation y equals negative 3x plus 2 again. Below this is the equation with 1 and negative 1 substituted for x and y, ready to be checked: negative 1 might equal negative 3 times 1 plus 2. Below this is negative 1 might equal negative 3 plus 2. Below this is negative 1 equals negative 1, with a check mark next to it. At the top of the fourth column is the value x equals negative 1. Below this is the equation y equals negative 3x plus 2. Below this is the equation with negative 1 substituted for x: y equals negative 3 times negative 1 plus 2. Below this is the equation simplified: y equals 3 plus 2. Below this is the equation solved: y equals 5. Below this is the ordered pair (negative 1, 5). Below this is the equation y equals negative 3x plus 2 again. Below this is the equation with negative 1 and 5 substituted for x and y, ready to be checked: 5 might equal negative 3 times negative 1 plus 2. Below this is 5 might equal 3 plus 2. Below this is 5 equals 5, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\"><\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><span id=\"eip-id1172188157425\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><span id=\"eip-id1172188157435\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><span id=\"eip-id1172188157445\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\">Substitute the value into the equation.<\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><span id=\"eip-id1172181443943\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><span id=\"eip-id1172181443953\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><span id=\"eip-id1172181443964\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\">Simplify.<\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><span id=\"eip-id1172181443980\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><span id=\"eip-id1172183445895\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><span id=\"eip-id1172183445905\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\">Simplify.<\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><span id=\"eip-id1172183445922\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><span id=\"eip-id1172183445932\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><span id=\"eip-id1172183445942\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038n_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\">Write the ordered pair.<\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><span id=\"eip-id1172184380866\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><span id=\"eip-id1172184380876\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><span id=\"eip-id1172184380887\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038o_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\">Check.<\/td>\n<td style=\"width: 24.2045%; height: 14px;\">(0, 2)<\/td>\n<td style=\"width: 21.8182%; height: 14px;\">(1, \u22121)<\/td>\n<td style=\"width: 23.9772%; height: 14px;\">(\u22121, 5)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\"><\/td>\n<td style=\"width: 24.2045%; height: 14px;\">\\(y=-3x+2\\)<\/td>\n<td style=\"width: 21.8182%; height: 14px;\">\\(y=-3x+2\\)<\/td>\n<td style=\"width: 23.9772%; height: 14px;\">\\(y=-3x+2\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 29.9183%; height: 30px;\" colspan=\"3\"><\/td>\n<td style=\"width: 24.2045%; height: 30px;\">\\(2\\stackrel{?}{=}-3\\cdot 0+2\\)<\/td>\n<td style=\"width: 21.8182%; height: 30px;\">\\(-1\\stackrel{?}{=}-3\\cdot 1+2\\)<\/td>\n<td style=\"width: 23.9772%; height: 30px;\">\\(5\\stackrel{?}{=}-3\\left(-1\\right)+2\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 29.9183%; height: 30px;\" colspan=\"3\"><\/td>\n<td style=\"width: 24.2045%; height: 30px;\">\\(2\\stackrel{?}{=}0+2\\)<\/td>\n<td style=\"width: 21.8182%; height: 30px;\">\\(-1\\stackrel{?}{=}-3+2\\)<\/td>\n<td style=\"width: 23.9772%; height: 30px;\">\\(5\\stackrel{?}{=}3+2\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\"><\/td>\n<td style=\"width: 24.2045%; height: 14px;\">\\(2=2\\checkmark\\)<\/td>\n<td style=\"width: 21.8182%; height: 14px;\">\\(-1=-1\\checkmark\\)<\/td>\n<td style=\"width: 23.9772%; height: 14px;\">\\(5=5\\checkmark\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596387161\">So, \\(\\left(0,2\\right)\\), \\(\\left(1,-1\\right)\\) and \\(\\left(-1,5\\right)\\) are all solutions to \\(y=-3x+2\\). We show them in table below.<span data-type=\"newline\">\n<\/span><\/p>\n\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><strong data-effect=\"bold\">\\(y=-3x+2\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(0,2\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(-1\\)<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(1,-1\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">\\(-1\\)<\/td>\n<td style=\"width: 81.4062px; text-align: center;\">5<\/td>\n<td style=\"width: 240.406px; text-align: center;\">\\(\\left(-1,5\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596756232\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596756237\" data-type=\"exercise\">\n<div id=\"fs-id1169596756239\" data-type=\"problem\">\n<p id=\"fs-id1169596756241\">Find three solutions to this equation: \\(y=-2x+3\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594028678\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594028680\">Answers will vary.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169594028723\">We have seen how using zero as one value of \\(x\\) makes finding the value of \\(y\\) easy. When an equation is in standard form, with both the \\(x\\) and \\(y\\) on the same side of the equation, it is usually easier to first find one solution when \\(x=0\\) find a second solution when \\(y=0\\), and then find a third solution.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594029355\" data-type=\"problem\">\n<p id=\"fs-id1169594029357\">Find three solutions to the equation \\(3x+2y=6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169596435800\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596435805\">We can substitute any value we want for \\(x\\) or any value for \\(y\\). Since the equation is in standard form, let\u2019s pick first \\(x=0\\), then \\(y=0\\), and then find a third point.<span data-type=\"newline\">\n<\/span><\/p>\n\n<table id=\"eip-id1172182678898\" style=\"width: 100%; height: 469px;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\"><\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172189391855\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172187698025\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172187698035\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\"><\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172187698051\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172187181962\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172187181972\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039n_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\">Substitute the value into the equation.<\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172182567983\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172182567994\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172182568004\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039o_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\">Simplify.<\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172185549081\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172185549090\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172185549100\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039p_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\">Solve.<\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172189367366\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172189367377\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172182380250\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039q_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\"><\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172182380265\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172182380276\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172187646915\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039r_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\">Write the ordered pair.<\/td>\n<td style=\"width: 153.406px;\" data-align=\"right\">(0, 3)<\/td>\n<td style=\"width: 139.406px;\" data-align=\"right\">(2, 0)<\/td>\n<td style=\"width: 126.406px;\" data-align=\"right\">\\(\\left(1,\\dfrac{3}{2}\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\">Check.<\/td>\n<td style=\"width: 153.406px;\" data-align=\"right\">\\(3x+2y=6\\)<\/td>\n<td style=\"width: 139.406px;\" data-align=\"right\">\\(3x+2y=6\\)<\/td>\n<td style=\"width: 126.406px;\" data-align=\"right\">\\(3x+2y=6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.4062px;\" colspan=\"3\" data-align=\"right\"><\/td>\n<td style=\"width: 153.406px;\" data-align=\"right\">\\(3\\cdot 0+2\\cdot 3\\stackrel{?}{=}6\\)<\/td>\n<td style=\"width: 139.406px;\" data-align=\"right\">\\(3\\cdot 2+2\\cdot 0\\stackrel{?}{=}6\\)<\/td>\n<td style=\"width: 126.406px;\" data-align=\"right\">\\(3\\cdot 1+2\\cdot \\frac{3}{2}\\stackrel{?}{=}6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.4062px;\" colspan=\"3\" data-align=\"right\"><\/td>\n<td style=\"width: 153.406px;\" data-align=\"right\">\\(0+6\\stackrel{?}{=}6\\)<\/td>\n<td style=\"width: 139.406px;\" data-align=\"right\">\\(6+0\\stackrel{?}{=}6\\)<\/td>\n<td style=\"width: 126.406px;\" data-align=\"right\">\\(3+3\\stackrel{?}{=}6\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.4062px;\" colspan=\"3\" data-align=\"right\"><\/td>\n<td style=\"width: 153.406px;\" data-align=\"right\">\\(6=6\\checkmark\\)<\/td>\n<td style=\"width: 139.406px;\" data-align=\"right\">\\(6=6\u2713\\)<\/td>\n<td style=\"width: 126.406px;\" data-align=\"right\">\\(6=6\u2713\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594079033\">So \\(\\left(0,3\\right)\\), \\(\\left(2,0\\right)\\), and \\(\\left(1,\\dfrac{3}{2}\\right)\\) are all solutions to the equation \\(3x+2y=6\\). We can list these three solutions in the table below.<span data-type=\"newline\">\n<\/span><\/p>\n\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\"><caption><strong data-effect=\"bold\">\\(3x+2y=6\\)<\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(0,3\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">\\(\\left(2,0\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">1<\/td>\n<td style=\"width: 81.4062px; text-align: center;\">\\(\\dfrac{3}{2}\\)<\/td>\n<td style=\"width: 240.406px; text-align: center;\">\\(\\left(1,\\frac{3}{2}\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594031694\" class=\"bc-section section\" data-depth=\"1\">\n<div id=\"fs-id1169594025622\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594025626\" data-type=\"exercise\">\n<div id=\"fs-id1169594025628\" data-type=\"problem\">\n<p id=\"fs-id1169594025630\">Find three solutions to the equation \\(2x+3y=6\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169594025652\" data-type=\"solution\"><details><summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594025654\">Answers will vary.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1169594122360\">\n \t<dt>linear equation<\/dt>\n \t<dd id=\"fs-id1169594122365\">A linear equation is of the form \\(Ax+By=C\\), where A and B are not both zero, is called a linear equation in two variables.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594122387\">\n \t<dt>ordered pair<\/dt>\n \t<dd id=\"fs-id1169594122393\">An ordered pair \\(\\left(x,y\\right)\\) gives the coordinates of a point in a rectangular coordinate system.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594122415\">\n \t<dt>origin<\/dt>\n \t<dd id=\"fs-id1169594122420\">The point \\(\\left(0,0\\right)\\) is called the origin. It is the point where the <em data-effect=\"italics\">x<\/em>-axis and <em data-effect=\"italics\">y<\/em>-axis intersect.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594132646\">\n \t<dt>quadrant<\/dt>\n \t<dd id=\"fs-id1169594132651\">The <em data-effect=\"italics\">x<\/em>-axis and the <em data-effect=\"italics\">y<\/em>-axis divide a plane into four regions, called quadrants.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594132666\">\n \t<dt>rectangular coordinate system<\/dt>\n \t<dd id=\"fs-id1169594132671\">A grid system is used in algebra to show a relationship between two variables; also called the <em data-effect=\"italics\">xy<\/em>-plane or the \u2018coordinate plane.\u2019<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594132682\">\n \t<dt><em data-effect=\"italics\">x<\/em>-coordinate<\/dt>\n \t<dd id=\"fs-id1169594132691\">The first number in an ordered pair \\(\\left(x,y\\right)\\).<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594132713\">\n \t<dt><em data-effect=\"italics\">y<\/em>-coordinate<\/dt>\n \t<dd id=\"fs-id1169594132723\">The second number in an ordered pair \\(\\left(x,y\\right)\\).<\/dd>\n<\/dl>\n<\/div>\n<h1>3.1 Exercise Set.<\/h1>\n<p id=\"fs-id1169595541833\">In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.<\/p>\n\n<ol class=\"twocolumn\">\n \t<li>\n<ol type=\"A\">\n \t<li>\\(\\left(-4,2\\right)\\)<\/li>\n \t<li>\\(\\left(-1,-2\\right)\\)<\/li>\n \t<li>\\(\\left(3,-5\\right)\\)<\/li>\n \t<li>\\(\\left(-3,5\\right)\\)<\/li>\n \t<li>\\(\\left(\\frac{5}{3},2\\right)\\)<\/li>\n<\/ol>\n<\/li>\n \t<li>\n<ol type=\"A\">\n \t<li><span data-type=\"newline\">\\(\\left(3,-1\\right)\\)<\/span><\/li>\n \t<li><span data-type=\"newline\">\\(\\left(-3,1\\right)\\)<\/span><\/li>\n \t<li><span data-type=\"newline\"> \\(\\left(-2,2\\right)\\)<\/span><\/li>\n \t<li>\\(\\left(0,4\\right)\\)<\/li>\n \t<li><span data-type=\"newline\">\\(\\left(1,\\frac{14}{5}\\right)\\)<\/span><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p id=\"fs-id1169594082455\">In the following exercises, plot each point in a rectangular coordinate system.<\/p>\n\n<ol class=\"twocolumn\" start=\"3\">\n \t<li>\n<ol type=\"A\">\n \t<li>\\(\\left(-2,0\\right)\\)<\/li>\n \t<li>\\(\\left(-3,0\\right)\\)<\/li>\n \t<li>\\(\\left(0,0\\right)\\)<\/li>\n \t<li>\\(\\left(-3,5\\right)\\)<\/li>\n \t<li>\\(\\left(0,2\\right)\\)<\/li>\n<\/ol>\n<\/li>\n \t<li>\n<ol type=\"A\">\n \t<li><span data-type=\"newline\">\\(\\left(0,0\\right)\\)<\/span><\/li>\n \t<li><span data-type=\"newline\">\\(\\left(0,-3\\right)\\)<\/span><\/li>\n \t<li><span data-type=\"newline\">\\(\\left(-4,0\\right)\\)<\/span><\/li>\n \t<li><span data-type=\"newline\"> \\(\\left(1,0\\right)\\)<\/span><\/li>\n \t<li><span data-type=\"newline\">\\(\\left(0,-2\\right)\\)<\/span><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p id=\"fs-id1169594008366\">In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.<\/p>\n\n<table class=\"no-lines\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">5.\n<div id=\"fs-id1169594008370\" class=\"material-set-2\" data-type=\"exercise\">\n<div id=\"fs-id1169594008372\" data-type=\"problem\"><span id=\"fs-id1169594008378\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 4, 1) is plotted and labeled \u201cA\u201d. The point (negative 3, negative 4) is plotted and labeled \u201cB\u201d. The point (1, negative 3) is plotted and labeled \u201cC\u201d. The point (4, 3) is plotted and labeled \u201cD\u201d.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_209_img_new.jpg\" alt=\"A graph plotting the points A (negative 4, 1), B (negative 3, negative 4), C (1, negative 3), D (4, 3).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/div><\/td>\n<td style=\"width: 50%;\">\n<div id=\"fs-id1169594041705\" class=\"material-set-2\" data-type=\"exercise\">\n<div data-type=\"problem\">6.<\/div>\n<\/div>\n<div id=\"fs-id1169594176002\" class=\"material-set-2\" data-type=\"exercise\">\n<div id=\"fs-id1169594176004\" data-type=\"problem\"><span id=\"fs-id1169594176010\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (0, negative 2) is plotted and labeled \u201cA\u201d. The point (negative 2, 0) is plotted and labeled \u201cB\u201d. The point (0, 5) is plotted and labeled \u201cC\u201d. The point (5, 0) is plotted and labeled \u201cD\u201d.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_211_img_new.jpg\" alt=\"A graph plotting the points A (0, negative 2), B (negative 2, 0), C (0, 5), D (5, 0).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\"><\/span><\/div>\n<\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169595582756\">In the following exercises, which ordered pairs are solutions to the given equations?<\/p>\n\n<ol class=\"twocolumn\" start=\"7\">\n \t<li>\\(2x+y=6\\)\n<ol type=\"A\">\n \t<li>\\(\\left(1,4\\right)\\)<\/li>\n \t<li>\\(\\left(3,0\\right)\\)<\/li>\n \t<li>\\(\\left(2,3\\right)\\)<\/li>\n<\/ol>\n<\/li>\n \t<li>\\(4x-2y=8\\)\n<ol type=\"A\">\n \t<li>\\(\\left(3,2\\right)\\)<\/li>\n \t<li>\\(\\left(1,4\\right)\\)<\/li>\n \t<li>\\(\\left(0,-4\\right)\\)<\/li>\n<\/ol>\n<\/li>\n \t<li>\\(y=4x+3\\)\n<ol type=\"A\">\n \t<li>\\(\\left(4,3\\right)\\)<\/li>\n \t<li>\\(\\left(-1,-1\\right)\\)<\/li>\n \t<li>\\(\\left(\\frac{1}{2},5\\right)\\)<\/li>\n<\/ol>\n<\/li>\n \t<li>\\(y=\\frac{1}{2}x-1\\)\n<ol type=\"A\">\n \t<li>\\(\\left(2,0\\right)\\)<\/li>\n \t<li>\\(\\left(-6,-4\\right)\\)<\/li>\n \t<li>\\(\\left(-4,-1\\right)\\)<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div id=\"fs-id1169596379766\" class=\"practice-perfect\" data-depth=\"2\">\n<p id=\"fs-id1169595272384\">In the following exercises, complete the table to find solutions to each linear equation.<\/p>\n\n<table class=\"no-lines\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 49.3711%;\">11. \\(y=2x-4\\)\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">\\(-1\\)<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 49.3711%;\">\n<p id=\"fs-id1169596635797\">\u00a012. \\(y=\\text{\u2212}x+5\\)<\/p>\n\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">\\(-2\\)<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.3711%;\">\n<div id=\"fs-id1169596635792\" data-type=\"exercise\">\n<div data-type=\"problem\"><\/div>\n<\/div>\n<div data-type=\"exercise\">\u00a013. \\(y=\\frac{1}{3}x+1\\)<\/div>\n<div id=\"fs-id1169594176646\" data-type=\"exercise\">\n<div id=\"fs-id1169594176648\" data-type=\"problem\">\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">6<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div><\/td>\n<td style=\"width: 49.3711%;\">\n<p id=\"fs-id1169594105772\">\u00a014. \\(y=-\\frac{3}{2}x-2\\)<\/p>\n\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">\\(-2\\)<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr style=\"height: 196px;\">\n<td style=\"width: 49.3711%; height: 196px;\">\n<p id=\"fs-id1169594031127\">15. \\(x+3y=6\\)<\/p>\n\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 49.3711%; height: 196px;\">\n<div id=\"fs-id1169596755278\" data-type=\"problem\">\n\n16. \\(2x-5y=10\\)\n\n<\/div>\n<div data-type=\"problem\">\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">10<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1169596647833\" data-type=\"exercise\">\n<div id=\"fs-id1169596647835\" data-type=\"problem\"><span style=\"orphans: 1; text-align: initial; font-size: 14pt;\">In the following exercises, find three solutions to each linear equation.<\/span><\/div>\n<ol class=\"twocolumn\" start=\"17\">\n \t<li data-type=\"problem\">\\(y=5x-8\\)<\/li>\n \t<li data-type=\"problem\">\\(y=-4x+5\\)<\/li>\n \t<li data-type=\"problem\">\\(x+y=8\\)<\/li>\n \t<li data-type=\"problem\">\\(x+y=-2\\)<\/li>\n \t<li data-type=\"problem\">\\(3x+y=5\\)<\/li>\n \t<li data-type=\"problem\">\\(4x-y=8\\)<\/li>\n \t<li data-type=\"problem\">\\(2x+4y=8\\)<\/li>\n \t<li data-type=\"problem\">\\(5x-2y=10\\)<\/li>\n<\/ol>\n<table class=\"no-lines\" style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169594006211\"><strong data-effect=\"bold\">25. <\/strong>\u00a0Mackenzie recorded her baby\u2019s weight every two months. The baby\u2019s age, in months, and weight, in pounds, are listed in the table below, and shown as an ordered pair in the third column.<\/p>\n<p id=\"fs-id1169594006220\"><span class=\"token\">a)<\/span>\u00a0Plot the points on a coordinate plane.<\/p>\n<span id=\"fs-id1171784026239\" data-type=\"media\" data-alt=\".\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_216_img_new.jpg\" alt=\"The x y axis with no points plotted.\" width=\"176\" height=\"160\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1171784026251\"><span class=\"token\">b)<\/span> Why is only Quadrant I needed?<\/p>\n\n<table id=\"fs-id1169594006239\" class=\"grid\" summary=\"This table has three columns. The top row is a header row, and each cell names the column below it. From left to right, the first column is labeled \u201cAge, x\u201d, the second column is labeled \u201cWeight, y\u201d, and the third column is labeled with the ordered pair (x, y). In the second row, the \u201cAge\u201d column contains 0, the \u201cWeight\u201d column contains 7, and the (x, y) column contains the ordered pair (0, 7). In the third row, the \u201cAge\u201d column contains 2, the \u201cWeight\u201d column contains 11, and the (x, y) column contains the ordered pair (0, 7). In the fourth row, the \u201cAge\u201d column contains 4, the \u201cWeight\u201d column contains 14, and the (x, y) column contains the ordered pair (4, 15). In the fifth row, the \u201cAge\u201d column contains 6, the \u201cWeight\u201d column contains 16, and the (x, y) column contains the ordered pair (6, 16). In the sixth row, the \u201cAge\u201d column contains 8, the \u201cWeight\u201d column contains 19, and the (x, y) column contains the ordered pair (8, 19). In the seventh row, the \u201cAge\u201d column contains 10, the \u201cWeight\u201d column contains 20, and the (x, y) column contains the ordered pair (10, 20). In the eighth row, the \u201cAge\u201d column contains 12, the \u201cWeight\u201d column contains 21, and the (x, y) column contains the ordered pair (12, 21).\">\n<tbody>\n<tr valign=\"top\">\n<th scope=\"col\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">Age \\(x\\)<\/strong><\/th>\n<th scope=\"col\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">Weight \\(y\\)<\/strong><\/th>\n<th scope=\"col\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/th>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">7<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(0, 7)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">11<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(2, 11)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">15<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(4, 15)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">6<\/td>\n<td data-valign=\"middle\" data-align=\"center\">16<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(6, 16)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">8<\/td>\n<td data-valign=\"middle\" data-align=\"center\">19<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(8, 19)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">10<\/td>\n<td data-valign=\"middle\" data-align=\"center\">20<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(10, 20)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">12<\/td>\n<td data-valign=\"middle\" data-align=\"center\">21<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(12, 21)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1.\n\n<span id=\"fs-id1169594030981\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 4, 2) is plotted and labeled &quot;a&quot;. The point (negative 1, negative 2) is plotted and labeled &quot;b&quot;. The point (3, negative 5) is plotted and labeled &quot;c&quot;. The point (negative 3, 5) is plotted and labeled \u201cd\u201d. The point (5 thirds, 2) is plotted and labeled \u201ce\u201d.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_201_img_new.jpg\" alt=\"A graph plotting the points a (negative 4, 2), b (negative 1, negative 2), c (3, negative 5), d (negative 3, 5), e (5 thirds, 2).\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\">\u00a0<\/span><\/td>\n<td style=\"width: 50%;\">2.\n\n<span id=\"fs-id1169594034148\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (3, negative 1) is plotted and labeled &quot;a&quot;. The point (negative 3, 1) is plotted and labeled &quot;b&quot;. The point (negative 2, 2) is plotted and labeled &quot;c&quot;. The point (negative 4, negative 3) is plotted and labeled \u201cd\u201d. The point (1, 14 fifths) is plotted and labeled \u201ce\u201d.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_203_img_new.jpg\" alt=\"A graph plotting the points a (3, negative 1), b (negative 3, 1), c (negative 2, 2), d (negative 4, negative 3), e (1, 14 fifths).\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3.\n\n<span id=\"fs-id1169596767368\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 2, 0) is plotted and labeled &quot;a&quot;. The point (negative 3, 0) is plotted and labeled &quot;b&quot;. The point (0, 0) is plotted and labeled &quot;c&quot;. The point (0, 4) is plotted and labeled \u201cd\u201d. The point (0, 3) is plotted and labeled \u201ce\u201d.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_205_img_new.jpg\" alt=\"A graph plotting the points a (negative 2, 0), b (negative 3, 0), c (0, 0), d (0, 4), e (0, 3).\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%;\">4.\n\n<span id=\"fs-id1169594031347\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (0, 0) is plotted and labeled &quot;a&quot;. The point (0, negative 3) is plotted and labeled &quot;b&quot;. The point (negative 4, 0) is plotted and labeled &quot;c&quot;. The point (1, 0) is plotted and labeled \u201cd\u201d. The point (0, negative 2) is plotted and labeled \u201ce\u201d.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_207_img_new.jpg\" alt=\"A graph plotting the points a (0, 0), b (0, negative 3), c (negative 4, 0), d (1, 0), e (0, negative 2).\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol class=\"twocolumn\" start=\"5\">\n \t<li>A: \\(\\left(-4,1\\right)\\)\u2003B: \\(\\left(-3,-4\\right)\\)\u2003C: \\(\\left(1,-3\\right)\\)\u2003D: \\(\\left(4,3\\right)\\)<\/li>\n \t<li>A: \\(\\left(0,-2\\right)\\)\u2003B: \\(\\left(-2,0\\right)\\)\u2003C: \\(\\left(0,5\\right)\\)\u2003D: \\(\\left(5,0\\right)\\)<\/li>\n \t<li>A, B<\/li>\n \t<li>A, C<\/li>\n \t<li>B, C<\/li>\n \t<li>A, B<\/li>\n<\/ol>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">11.\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 62px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">\\(-4\\)<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(0,-4\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 20px; text-align: center;\">2<\/td>\n<td style=\"width: 14.1766%; height: 20px; text-align: center;\">0<\/td>\n<td style=\"width: 11.8073%; height: 20px; text-align: center;\">\\(\\left(2,0\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">\\(-1\\)<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">\\(-6\\)<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(-1,-6\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">12.\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 66px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">5<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(0,5\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 24px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 24px; text-align: center;\">2<\/td>\n<td style=\"width: 11.8073%; height: 24px; text-align: center;\">\\(\\left(3,2\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">\\(-2\\)<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">7<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(-2,7\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">13.\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">1<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(0,1\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(3,2\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">6<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(6,3\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">14.\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">\\(-2\\)<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(0,-2\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">\\(-5\\)<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(2,-5\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">\\(-2\\)<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">1<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(-2,1\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">15.\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(0,2\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">4<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(3,1\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">6<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(6,0\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 33.3333%; height: 15px;\">16.\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(x\\)<\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(y\\)<\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\">\\(\\left(x,y\\right)\\)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">\\(-2\\)<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(0,-2\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">10<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(10,2\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">5<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\">\\(\\left(5,0\\right)\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol class=\"twocolumn\" start=\"17\">\n \t<li>Answers will vary.<\/li>\n \t<li>Answers will vary.<\/li>\n \t<li>Answers will vary.<\/li>\n \t<li>Answers will vary.<\/li>\n \t<li>Answers will vary.<\/li>\n \t<li>Answers will vary.<\/li>\n \t<li>Answers will vary.<\/li>\n \t<li>Answers will vary.<\/li>\n<\/ol>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 306px;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\">25.\n<p id=\"fs-id1169594249629\"><span class=\"token\">a)<\/span><span data-type=\"newline\">\n<\/span><\/p>\n<span id=\"fs-id1169594249634\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from 0 to 25. The points (0, 7), (2, 11), (4, 15), (6, 16), (8, 19), (10, 20) and (12, 21) are plotted and labeled.\"><img class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_213_img_new.jpg\" alt=\"A graph that plots the points (0, 7), (2, 11), (4, 15), (6, 16), (8, 19), (10, 20) and (12, 21).\" width=\"176\" height=\"160\" data-media-type=\"image\/jpeg\"><\/span>\n\n<span class=\"token\">b)<\/span> Age and weight are only positive.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cUse the Rectangular Coordinate System\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Adaptation Statement for more information.","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section it is expected that you will be able to:<\/p>\n<ul>\n<li>Plot points in a rectangular coordinate system<\/li>\n<li>Verify solutions to an equation in two variables<\/li>\n<li>Complete a table of solutions to a linear equation<\/li>\n<li>Find solutions to a linear equation in two variables<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Plot Points on a Rectangular Coordinate System<\/h1>\n<p>Just like maps use a grid system to identify locations, a grid system is used in algebra to show a relationship between two variables in a <strong>rectangular coordinate system<\/strong>. The rectangular coordinate system is also called the <em data-effect=\"italics\">xy<\/em>-plane or the \u2018coordinate plane.\u2019<\/p>\n<p>The horizontal number line is called the <em data-effect=\"italics\">x-axis<\/em>. The vertical number line is called the <em data-effect=\"italics\">y-axis.<\/em> The <em data-effect=\"italics\">x<\/em>-axis and the <em data-effect=\"italics\">y<\/em>-axis together form the rectangular coordinate system. These axes divide a plane into four regions, called <strong data-effect=\"bold\">quadrants<\/strong>. The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise. See <a href=\"#CNX_ElemAlg_Figure_04_01_001\">(Figure 1)<\/a>.<\/p>\n<p>\u2018Quadrant\u2019 has the root \u2018quad,\u2019 which means \u2018four.\u2019<\/p>\n<figure style=\"width: 342px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2020\/08\/CNX_ElemAlg_Figure_04_01_001_img_new.jpg\" alt=\"Described in previous paragraphs. Top right quadrant labelled \u201cI\u201d, top left \u201cII\u201d, bottom left \u201cIII\u201d, and bottom right \u201cIV\u201d.\" width=\"342\" height=\"351\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .1<\/figcaption><\/figure>\n<p>In the <span class=\"no-emphasis\" data-type=\"term\">rectangular coordinate system<\/span>, every point is represented by an <em data-effect=\"italics\">ordered pair<\/em>. The first number in the ordered pair is the\u00a0<span data-type=\"term\"><strong><em data-effect=\"italics\">x<\/em>-coordinate<\/strong><\/span> of the point, and the second number is the <strong><em data-effect=\"italics\">y<\/em>-coordinate<\/strong> of the point.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Ordered pair<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>An ordered pair, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/>,\u00a0 gives the coordinates of a point in a rectangular coordinate system.<span id=\"fs-id1169596440557\" data-type=\"media\" data-alt=\"The ordered pair x y is labeled with the first coordinate x labeled as &quot;x-coordinate&quot; and the second coordinate y labeled as &quot;y-coordinate&quot;.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_033_img_new.jpg\" alt=\"Ordered pair x y. The first coordinate x labeled &quot;x-coordinate&quot;, the second coordinate y labeled &quot;y-coordinate&quot;.\" width=\"250\" height=\"59\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p style=\"text-align: left;\">The first number is the x-coordinate.<\/p>\n<p class=\"hanging-indent\">The second number is the y-coordinate.<\/p>\n<\/div>\n<\/div>\n<p>The phrase \u2018ordered pair\u2019 means the order is important. What is the ordered pair of the point where the axes cross? At that point both coordinates are zero, so its ordered pair is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>. The point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> has a special name. It is called the <strong><span class=\"no-emphasis\" data-type=\"term\">origin<\/span><\/strong>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">The origin<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> is called the <span data-type=\"term\">origin<\/span>. It is the point where the <em data-effect=\"italics\">x<\/em>-axis and <em data-effect=\"italics\">y<\/em>-axis intersect.<\/p>\n<\/div>\n<\/div>\n<p>We use the coordinates to locate a point on the <em data-effect=\"italics\">xy<\/em>-plane. Let\u2019s plot the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-450ee1faefebebc715b20a97daae94ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> as an example. First, locate 1 on the <em data-effect=\"italics\">x<\/em>-axis and lightly sketch a vertical line through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/>. Then, locate 3 on the <em data-effect=\"italics\">y<\/em>-axis and sketch a horizontal line through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8e36d35d8563f5053efd9935e88634f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>. Now, find the point where these two lines meet\u2014that is the point with coordinates <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-450ee1faefebebc715b20a97daae94ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<figure style=\"width: 301px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_002_img_new.jpg\" alt=\"Figure 2. The result of the process described in previous paragraph plotting the point (1,3).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .2<\/figcaption><\/figure>\n<p>Notice that the vertical line through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/> and the horizontal line through <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8e36d35d8563f5053efd9935e88634f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/> are not part of the graph. We just used them to help us locate the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-450ee1faefebebc715b20a97daae94ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Plot each point in the rectangular coordinate system and identify the <span class=\"no-emphasis\" data-type=\"term\">quadrant<\/span> in which the point is located:<\/p>\n<p><span class=\"token\">A <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cf0ffd7a31e177b4a3caa16a8b3141b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">B <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9523da542e5bfc81814e047c926984c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">C <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1564d1d2328bb6bd9e7b30e6d573d2fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">D <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6fd7f677a681964debbd5fb9bbb3c944_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">E <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1c98a0c2caafdf0d2bb0cfb73e36a2a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"40\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<p><strong>Solution<br \/>\n<\/strong><\/p>\n<p>The first number of the coordinate pair is the <em data-effect=\"italics\">x<\/em>-coordinate, and the second number is the <em data-effect=\"italics\">y<\/em>-coordinate.<\/p>\n<ol type=\"A\">\n<li>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d3e213d8d687e32831c24e16c432b60e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/>, the point is to the left of the <em data-effect=\"italics\">y<\/em>-axis. Also, since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0621c4f761e7864714642fcc62d4c42f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>, the point is above the <em data-effect=\"italics\">x<\/em>-axis. The point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cf0ffd7a31e177b4a3caa16a8b3141b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> is in Quadrant II.<\/li>\n<li>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7e135cd6350a4c21195c621240f7aee7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/>, the point is to the left of the <em data-effect=\"italics\">y<\/em>-axis. Also, since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-53923be0c534e9cf06b453317eed3f30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/>, the point is below the <em data-effect=\"italics\">x<\/em>-axis. The point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9523da542e5bfc81814e047c926984c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/> is in Quadrant III.<\/li>\n<li>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/>, the point is to the right of the <em data-effect=\"italics\">y<\/em>-axis. Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-91f9ec631e44f3d108457c2f8adad27c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/>, the point is below the <em data-effect=\"italics\">x<\/em>-axis. The point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1564d1d2328bb6bd9e7b30e6d573d2fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/> is in Quadrant lV.<\/li>\n<li>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/>, the point is to the left of the <em data-effect=\"italics\">y<\/em>-axis. Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8e36d35d8563f5053efd9935e88634f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>, the point is above the <em data-effect=\"italics\">x<\/em>-axis. The point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6fd7f677a681964debbd5fb9bbb3c944_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> is in Quadrant II.<\/li>\n<li>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, the point is to the right of the <em data-effect=\"italics\">y<\/em>-axis. Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ea14ccb92283ed95e64b9feb53c6da2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/>, the point is above the <em data-effect=\"italics\">x<\/em>-axis. (It may be helpful to write <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3c8a34714cd9e14f96438eaca16625df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> as a mixed number or decimal.) The point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1c98a0c2caafdf0d2bb0cfb73e36a2a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"40\" style=\"vertical-align: -7px;\" \/> is in Quadrant I.<span data-type=\"newline\"><br \/>\n<\/span><\/li>\n<\/ol>\n<p id=\"CNX_ElemAlg_Figure_04_01_003\" class=\"bc-figure figure indent hanging-indent\"><span id=\"fs-id1169596298887\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 5, 4), (negative 2, 3), (negative 3, negative 4), (3, five halves), and (2, negative 3) are plotted and labeled.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_003_img_new.jpg\" alt=\"A graph plotting the points (-5, 4), (-2, 3), (-3, -4), (3, 5\/2), and (2, -3).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Plot each point in a rectangular coordinate system and identify the quadrant in which the point is located:<\/p>\n<p><span class=\"token\">A <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">B <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d29d505cec09336aa569e1cca8670699_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">C <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8680e4f49775c6a5702e20f9a2e105a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">D <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6bd03bb09a34e49dd9f3ebf548e3dab1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">E <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6b3e4a390b9705038aecd2ab7d812a5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"53\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p><span id=\"fs-id1169596376606\" data-type=\"solution\"><span id=\"fs-id1169594008202\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 2, 1) is plotted and labeled &quot;a&quot;. The point (negative 3, negative 1) is plotted and labeled &quot;b&quot;. The point (4, negative 4) is plotted and labeled &quot;c&quot;. The point (negative 4, negative one half) is plotted and labeled \u201cd\u201d.\"><span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_026_img_new.jpg\" alt=\"A graph plotting the points described in the previous paragraph.\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\" \/><\/span><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<p>How do the signs affect the location of the points? You may have noticed some patterns as you graphed the points in the previous example.<\/p>\n<p>For the point in <a class=\"autogenerated-content\" href=\"#fs-id1169596587993\">(Figure 2)<\/a> in Quadrant IV, what do you notice about the signs of the coordinates? What about the signs of the coordinates of points in the third quadrant? The second quadrant? The first quadrant?<\/p>\n<p>Can you tell just by looking at the coordinates in which quadrant the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-edd8d8b57c2815309edbd447803c95fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> is located? In which quadrant is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c02ba61efe13be423bc75f83a9846930_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/> located?<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Quadrants<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>We can summarize sign patterns of the quadrants in this way.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0a155aa1538052979c1dd5330bcb76ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#81;&#117;&#97;&#100;&#114;&#97;&#110;&#116;&#32;&#73;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#81;&#117;&#97;&#100;&#114;&#97;&#110;&#116;&#32;&#73;&#73;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#81;&#117;&#97;&#100;&#114;&#97;&#110;&#116;&#32;&#73;&#73;&#73;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#81;&#117;&#97;&#100;&#114;&#97;&#110;&#116;&#32;&#73;&#86;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#43;&#44;&#43;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#44;&#43;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#43;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"429\" style=\"vertical-align: -27px;\" \/><\/p>\n<p><span id=\"fs-id1169596767978\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The top-right portion of the plane is labeled &quot;I&quot; and &quot;ordered pair +, +&quot;, the top-left portion of the plane is labeled &quot;II&quot; and &quot;ordered pair -, +&quot;, the bottom-left portion of the plane is labelled &quot;III&quot; &quot;ordered pair -, -&quot; and the bottom-right portion of the plane is labeled &quot;IV&quot; and &quot;ordered pair +, -&quot;.\"><span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\"><span id=\"fs-id1169596298887\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 5, 4), (negative 2, 3), (negative 3, negative 4), (3, five halves), and (2, negative 3) are plotted and labeled.\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> <\/span><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_004_img_new.jpg\" alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The graph shows the x y-coordinate plane. The x and y-axis each run from -7 to 7. The top-right portion of the plane is labeled &quot;I&quot; and &quot;ordered pair +, +&quot;, the top-left portion of the plane is labeled &quot;II&quot; and &quot;ordered pair -, +&quot;, the bottom-left portion of the plane is labelled &quot;III&quot; &quot;ordered pair -, -&quot; and the bottom-right portion of the plane is labeled &quot;IV&quot; and &quot;ordered pair +, -&quot;.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<p>What if one coordinate is zero as shown in <a class=\"autogenerated-content\" href=\"#CNX_ElemAlg_Figure_04_01_005\">(Figure 3)<\/a>? Where is the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e2c3a69d33f9737210f9c4f1551f4b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> located? Where is the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dd6f8f312ab67ad0422a4959540654f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> located?<span data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. Points (0, 4) and (negative 2, 0) are plotted and labeled.\"><span data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. Points (0, 4) and (negative 2, 0) are plotted and labeled.\"><span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\"><span id=\"fs-id1169596298887\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 5, 4), (negative 2, 3), (negative 3, negative 4), (3, five halves), and (2, negative 3) are plotted and labeled.\"> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span> <\/span><\/span><\/span><\/p>\n<figure style=\"width: 301px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_005_img_new.jpg\" alt=\"A graph plotting the points (0, 4) and (negative 2, 0).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure .3<span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\"> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/figcaption><\/figure>\n<p>The point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e2c3a69d33f9737210f9c4f1551f4b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> is on the <em data-effect=\"italics\">y<\/em>-axis and the point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dd6f8f312ab67ad0422a4959540654f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> is on the <em data-effect=\"italics\">x<\/em>-axis.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Points on the axes<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Points with a <span class=\"no-emphasis\" data-type=\"term\"><em data-effect=\"italics\">y<\/em>-coordinate<\/span> equal to 0 are on the <em data-effect=\"italics\">x<\/em>-axis, and have coordinates <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-53d4347201ab8f9c6f195eeec4b01f0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p>Points with an <span class=\"no-emphasis\" data-type=\"term\"><em data-effect=\"italics\">x<\/em>-coordinate<\/span> equal to 0 are on the <em data-effect=\"italics\">y<\/em>-axis, and have coordinates <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-05dbabd42fe84ba97e673be0628c5974_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"37\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Plot each point:<span class=\"token\">A <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6655aef23bcf82d48b1ff5bf888d5b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">B <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2809647061e2f05aa3080110836f8805_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">C <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7ba9cc2a7f12e65a6b3de8f34bcc16e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">D <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">E <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ec6084fa217f87f8fc5df481ca60ccf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><strong>Solution<\/strong><\/p>\n<ol id=\"fs-id1169597525788\" class=\"circled\" type=\"A\">\n<li>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, the point whose coordinates are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6655aef23bcf82d48b1ff5bf888d5b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> is on the <em data-effect=\"italics\">y<\/em>-axis.<\/li>\n<li>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>, the point whose coordinates are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2809647061e2f05aa3080110836f8805_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> is on the <em data-effect=\"italics\">x<\/em>-axis.<\/li>\n<li>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>, the point whose coordinates are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7ba9cc2a7f12e65a6b3de8f34bcc16e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> is on the <em data-effect=\"italics\">x<\/em>-axis.<\/li>\n<li>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>, the point whose coordinates are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> is the origin.<\/li>\n<li>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, the point whose coordinates are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ec6084fa217f87f8fc5df481ca60ccf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/> is on the <em data-effect=\"italics\">y<\/em>-axis.<span data-type=\"newline\"><br \/>\n<\/span><span id=\"fs-id1169596653858\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 3, 0), (0, 0), (0, negative 1), (0, 5), and (4, 0) are plotted and labeled.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_006_img_new.jpg\" alt=\"A graph plotting the points (negative 3, 0), (0, 0), (0, negative 1), (0, 5), and (4, 0).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Plot each point:<span class=\"token\">A <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2809647061e2f05aa3080110836f8805_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">B <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dd6f8f312ab67ad0422a4959540654f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">C <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">D <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-398828550549fdd4b2191f8f7cde7bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">E <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-017f20ea0c6fda3470cedb20ea0b5537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p><span id=\"fs-id1169596654134\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled.\"><span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/span> <img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_028_img_new.jpg\" alt=\"A graph plotting the points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3).\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/details>\n<\/div>\n<\/div>\n<p>In algebra, being able to identify the coordinates of a point shown on a graph is just as important as being able to plot points. To identify the <em data-effect=\"italics\">x<\/em>-coordinate of a point on a graph, read the number on the <em data-effect=\"italics\">x<\/em>-axis directly above or below the point. To identify the <em data-effect=\"italics\">y<\/em>-coordinate of a point, read the number on the <em data-effect=\"italics\">y<\/em>-axis directly to the left or right of the point. Remember, when you write the <span class=\"no-emphasis\" data-type=\"term\">ordered pair<\/span> use the correct order, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Name the ordered pair of each point shown in the rectangular coordinate system.<span id=\"fs-id1169596453833\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled A, B, C, D, and E, respectively.\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_007_img_new.jpg\" alt=\"Described in following paragraph.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Point A is above <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> on the <em data-effect=\"italics\">x<\/em>-axis, so the <em data-effect=\"italics\">x<\/em>-coordinate of the point is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<ul id=\"fs-id1169594050927\" data-bullet-style=\"bullet\">\n<li>The point is to the left of 3 on the <em data-effect=\"italics\">y<\/em>-axis, so the <em data-effect=\"italics\">y<\/em>-coordinate of the point is 3.<\/li>\n<li>The coordinates of the point are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-03125d47f1e456b2a5c3479daa28f59c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<\/ul>\n<p id=\"fs-id1169594155473\">Point B is below <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/> on the <em data-effect=\"italics\">x<\/em>-axis, so the <em data-effect=\"italics\">x<\/em>-coordinate of the point is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<ul id=\"fs-id1169594029277\" data-bullet-style=\"bullet\">\n<li>The point is to the left of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> on the <em data-effect=\"italics\">y<\/em>-axis, so the <em data-effect=\"italics\">y<\/em>-coordinate of the point is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li>The coordinates of the point are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-659f5d2dee5bcea4b83fdb4d330c9b96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<\/ul>\n<p id=\"fs-id1169596555335\">Point C is above 2 on the <em data-effect=\"italics\">x<\/em>-axis, so the <em data-effect=\"italics\">x<\/em>-coordinate of the point is 2.<\/p>\n<ul id=\"fs-id1169596282410\" data-bullet-style=\"bullet\">\n<li>The point is to the right of 4 on the <em data-effect=\"italics\">y<\/em>-axis, so the <em data-effect=\"italics\">y<\/em>-coordinate of the point is 4.<\/li>\n<li>The coordinates of the point are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-65c84a7e1d884e51e9ff8e8338318a74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<\/ul>\n<p id=\"fs-id1169594159149\">Point D is below 4 on the <em data-effect=\"italics\">x<\/em>-axis, so the <em data-effect=\"italics\">x<\/em>-coordinate of the point is 4.<\/p>\n<ul id=\"fs-id1169594078395\" data-bullet-style=\"bullet\">\n<li>The point is to the right of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> on the <em data-effect=\"italics\">y<\/em>-axis, so the <em data-effect=\"italics\">y<\/em>-coordinate of the point is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e344351eb8a6a075b3d1df3943b3d637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: -1px;\" \/><\/li>\n<li>The coordinates of the point are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8680e4f49775c6a5702e20f9a2e105a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>.<\/li>\n<\/ul>\n<p id=\"fs-id1169596393241\">Point E is on the <em data-effect=\"italics\">y<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f986dbfac9d3f29a18cba91e9efa9d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/>. The coordinates of point E are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f644d689ddf634b480d4ff320ff89c7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"fs-id1169594050420\">Point F is on the <em data-effect=\"italics\">x<\/em>-axis at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3573bf1ea4c223bb71878796b2106731_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>. The coordinates of point F are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fc6a40acab1fcbe9adecd900d5d2a756_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"45\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Name the ordered pair of each point shown in the rectangular coordinate system.<span id=\"fs-id1169594087555\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled A, B, C, D, and E, respectively.\"><span id=\"fs-id1169596446654\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. An arrow starts at the origin and extends right to the number 2 on the x-axis. The point (1, 3) is plotted and labeled. Two dotted lines, one parallel to the x-axis, the other parallel to the y-axis, meet perpendicularly at 1, 3. The dotted line parallel to the x-axis intercepts the y-axis at 3. The dotted line parallel to the y-axis intercepts the x-axis at 1.\"><span id=\"fs-id1169596453833\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The points (4, 0), (negative 2, 0), (0, 0), (0, 2), and (0, negative 3) are plotted and labeled A, B, C, D, and E, respectively.\"><span id=\"fs-id1169596653858\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 3, 0), (0, 0), (0, negative 1), (0, 5), and (4, 0) are plotted and labeled.\"><span id=\"fs-id1169596298887\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 7 to 7. The points (negative 5, 4), (negative 2, 3), (negative 3, negative 4), (3, five halves), and (2, negative 3) are plotted and labeled.\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/span><\/span> <\/span><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_030_img_new.jpg\" alt=\"A graph plotting the points (5, 1), (negative 2, 4), (negative 5, negative 1), (3, negative 2), (0, negative 5) labelled A-E.\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596446575\">A: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b932df7404bba7c4812c40fc6d0d4b4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003B: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8ab12b849de44ae6a90ccee83f8e1018_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>\u2003C: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ebf0fa586cc0702253c6470f89802b99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/>\u2003D: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dbaec542907415eac32615dfae0ae911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>\u2003E: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5f6ab1a0ed415088c10eaaa3977a4992_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>\u2003F: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2809647061e2f05aa3080110836f8805_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<h1>Verify Solutions to an Equation in Two Variables<\/h1>\n<p>Up to now, all the equations you have solved were equations with just one variable. In almost every case, when you solved the equation you got exactly one solution. The process of solving an equation ended with a statement like <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/>. (Then, you checked the solution by substituting back into the equation.)<br \/>\nHere\u2019s an example of an equation in one variable, and its one solution.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e4e60aacfd2b0bb1229a2c11b2728ec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#120;&#43;&#53;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#120;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#49;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#120;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"114\" style=\"vertical-align: -23px;\" \/><\/p>\n<p>But equations can have more than one variable. Equations with two variables may be of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>. Equations of this form are called <strong data-effect=\"bold\">linear equations in two variables<\/strong>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Linear equation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>An equation of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> are not both zero, is called a <span data-type=\"term\">linear equation<\/span> <strong data-effect=\"bold\">in two variables<\/strong>.<\/p>\n<\/div>\n<\/div>\n<p>Notice the word <em data-effect=\"italics\">line<\/em> in <strong data-effect=\"bold\">linear<\/strong>. Here is an example of a linear equation in two variables, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><span id=\"fs-id1169596652462\" data-type=\"media\" data-alt=\"In this figure, we see the linear equation Ax plus By equals C. Below this is the equation x plus 4y equals 8. Below this are the values A equals 1, B equals 4, and C equals 8.\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_032_img_new.jpg\" alt=\"In this figure, we see the linear equation Ax plus By equals C. Below this is the equation x plus 4y equals 8. Below this are the values A equals 1, B equals 4, and C equals 8.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596240065\">The equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9ca7e6824e1b3783daf117b3e7f97530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\" \/> is also a <span class=\"no-emphasis\" data-type=\"term\">linear equation<\/span>. But it does not appear to be in the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>. We can use the Addition Property of Equality and rewrite it in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/> form.<\/p>\n<table id=\"eip-439\" style=\"width: 100%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9ca7e6824e1b3783daf117b3e7f97530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add to both sides.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-08c3c2e666d751b0164ce0198cba773b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#51;&#120;&#61;&#45;&#51;&#120;&#43;&#53;&#43;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"178\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e2fbda3b6e2cbcb6f470db9a04369482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#51;&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to put it in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/> form.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f5e5d8d536bd15610418e85b413562ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594031828\">By rewriting <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9ca7e6824e1b3783daf117b3e7f97530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f5e5d8d536bd15610418e85b413562ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/>, we can easily see that it is a linear equation in two variables because it is of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>. When an equation is in the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>, we say it is in <em data-effect=\"italics\">standard form<\/em>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Standard Form of Linear Equation<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A linear equation is in standard form when it is written <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<p>Most people prefer to have <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f34f74d98915e33f37a086f8cbfb996a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> be integers and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c7c76516e02e800674d79e291782f797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#92;&#103;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"46\" style=\"vertical-align: -3px;\" \/> when writing a linear equation in standard form, although it is not strictly necessary.<\/p>\n<p>Linear equations have infinitely many solutions. For every number that is substituted for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> there is a corresponding <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> value. This pair of values is a <em data-effect=\"italics\">solution<\/em> to the linear equation and is represented by the ordered pair <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/>. When we substitute these values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> into the equation, the result is a true statement, because the value on the left side is equal to the value on the right side.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Solution of a Linear Equation in Two Variables<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>An <span data-type=\"term\">ordered pair<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/> is a <strong data-effect=\"bold\">solution<\/strong> of the linear equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>, if the equation is a true statement when the <em data-effect=\"italics\">x<\/em>&#8211; and <em data-effect=\"italics\">y<\/em>-values of the ordered pair are substituted into the equation.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Determine which ordered pairs are solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-971440700f82c87567aa141fb48186a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#52;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p>A (\\left(0,2\\right)\\)\u2003B <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d5b80bc57d91ba9e2936cc72d75618b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>\u2003C <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4d4c06de3c48d63deaeaa1d43ed2ba09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Substitute the x- and y-values from each ordered pair into the equation and determine if the result is a true statement.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_034_img_new.jpg\" alt=\"This figure has three columns. At the top of the first column is the ordered pair (0, 2). Below this are the values x equals 0 and y equals 2. Below this is the equation x plus 4y equals 8. Below this is the same equation with 0 and 2 substituted for x and y: 0 plus 4 times 2 might equal 8. Below this is 0 plus 8 might equal 8. Below this is 8 equals 8 with a check mark next to it. Below this is the sentence \u201c(0, 2) is a solution.\u201d At the top of the second column is the ordered pair (2, negative 4). Below this are the values x equals 2 and y equals negative 4. Below this is the equation x plus 4y equals 8. Below this is the same equation with 2 and negative 4 substituted for x and y: 2 plus 4 times negative 4 might equal 8. Below this is 2 plus negative 16 might equal 8. Below this is negative 14 does not equal 8. Below this is the sentence: \u201c(2, negative 4) is not a solution.\u201d At the top of the third column is the ordered pair (negative 4, 3). Below this are the values x equals negative 4 and y equals 3. Below this is the equation x plus 4y equals 8. Below this is the same equation with negative 4 and 3 substituted for x and y: negative 4 plus 4 times 3 might equal 8. Below this is negative 4 plus 12 might equal 8. Below this is 8 equals 8 with a check mark next to it. Below this is the sentence: \u201c(negative 4, 3) is a solution.\u201d\" data-media-type=\"image\/jpeg\" \/><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Which of the following ordered pairs are solutions to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-07795f3421886c79416fa26cd22cc5f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>?<br \/>\n<span class=\"token\">A <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-28a186f2424d2e935d6aa6388441b6d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">B <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-559928bd7c8949c8342dd73437aef05a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">C <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e228594fa0479f071602af78e20058a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/p>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596655873\">A, C<\/p>\n<\/details>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Which of the following ordered pairs are solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e97f6bd16e4dfbf96ffc41bc5250fd2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/>?<\/p>\n<p><span class=\"token\">A <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ec6084fa217f87f8fc5df481ca60ccf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">B <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ab73a57c5e039ffb22ed1a8e29747bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">C <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d912edffbf9f66f30a875028acf7b8fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>Substitute the <em data-effect=\"italics\">x<\/em>&#8211; and <em data-effect=\"italics\">y<\/em>-values from each <span class=\"no-emphasis\" data-type=\"term\">ordered pair<\/span> into the equation and determine if it results in a true statement.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-id1169596658144\" data-type=\"media\" data-alt=\"This figure has three columns. At the top of the first column is the ordered pair (0, negative 1). Below this are the values x equals 0 and y equals negative 1. Below this is the equation y equals 5x minus 1. Below this is the same equation with 0 and negative 1 substituted for x and y: negative 1 might equal 5 times 0 minus 1. Below this is negative 1 might equal 0 minus 1. Below this is negative 1 equals negative 1 with a check mark next to it. Below this is the sentence: \u201c(0, negative 1) is a solution.\u201d At the top of the second column is the ordered pair (1, 4). Below this are the values x equals 1 and y equals 4. Below this is the equation y equals 5x minus 1. Below this is the same equation with 1 and 4 substituted for x and y: 4 might equal 5 times 1 minus 1. Below this is 4 might equal 5 minus 1. Below this is 4 equals 4 with a check mark next to it. Below this is the sentence: \u201c(1, 4) is a solution.\u201d At the top of the right column is the ordered pair (negative 2, negative 7). Below this are the values x equals negative 2 and y equals negative 7. Below this is the equation y equals 5x minus 1. Below this is the same equation with negative 2 and negative 7 substituted for x and y: negative 7 might equal 5 times negative 2 minus 1. Below this is negative 7 might equal negative 10 minus 1. Below this is negative 7 does not equal negative 11. Below this is the sentence: \u201c(negative 2, negative 7) is not a solution.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_035_img_new.jpg\" alt=\"This figure has three columns. At the top of the first column is the ordered pair (0, negative 1). Below this are the values x equals 0 and y equals negative 1. Below this is the equation y equals 5x minus 1. Below this is the same equation with 0 and negative 1 substituted for x and y: negative 1 might equal 5 times 0 minus 1. Below this is negative 1 might equal 0 minus 1. Below this is negative 1 equals negative 1 with a check mark next to it. Below this is the sentence: \u201c(0, negative 1) is a solution.\u201d At the top of the second column is the ordered pair (1, 4). Below this are the values x equals 1 and y equals 4. Below this is the equation y equals 5x minus 1. Below this is the same equation with 1 and 4 substituted for x and y: 4 might equal 5 times 1 minus 1. Below this is 4 might equal 5 minus 1. Below this is 4 equals 4 with a check mark next to it. Below this is the sentence: \u201c(1, 4) is a solution.\u201d At the top of the right column is the ordered pair (negative 2, negative 7). Below this are the values x equals negative 2 and y equals negative 7. Below this is the equation y equals 5x minus 1. Below this is the same equation with negative 2 and negative 7 substituted for x and y: negative 7 might equal 5 times negative 2 minus 1. Below this is negative 7 might equal negative 10 minus 1. Below this is negative 7 does not equal negative 11. Below this is the sentence: \u201c(negative 2, negative 7) is not a solution.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Which of the following ordered pairs are solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-da6fdd764c10cd72cb8a7592107763ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/>? <span class=\"token\">A <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ef24d382319a3ce81f280194edba003a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">B <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-745bd1150b5c3e65ae8bad5282a5b3b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003<span class=\"token\">C <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7a98d0e71a22be78d161caf964026b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169596658490\">B<\/p>\n<\/details>\n<\/div>\n<\/div>\n<h1>Complete a Table of Solutions to a Linear Equation in Two Variables<\/h1>\n<p id=\"fs-id1169596684664\">In the examples above, we substituted the <em data-effect=\"italics\">x<\/em>&#8211; and <em data-effect=\"italics\">y<\/em>-values of a given ordered pair to determine whether or not it was a solution to a linear equation. But how do you find the ordered pairs if they are not given? It\u2019s easier than you might think\u2014you can just pick a value for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and then solve the equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>. Or, pick a value for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> and then solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1169596243344\">We\u2019ll start by looking at the solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e97f6bd16e4dfbf96ffc41bc5250fd2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/> that we found in <a class=\"autogenerated-content\" href=\"#fs-id1169596400539\">(Example 5)<\/a>. We can summarize this information in a table of solutions, as shown in <a class=\"autogenerated-content\" href=\"#fs-id1169594029160\">(Table 1)<\/a>.<\/p>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"height: 64px; width: 457px;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e97f6bd16e4dfbf96ffc41bc5250fd2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/strong><\/span><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 75.7344px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/span><\/td>\n<td style=\"width: 83.8125px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/span><\/td>\n<td style=\"width: 249.172px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 75.7344px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">0<\/span><\/td>\n<td style=\"width: 83.8125px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/span><\/td>\n<td style=\"width: 249.172px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ec6084fa217f87f8fc5df481ca60ccf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 75.7344px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">1<\/span><\/td>\n<td style=\"width: 83.8125px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">4<\/span><\/td>\n<td style=\"width: 249.172px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ab73a57c5e039ffb22ed1a8e29747bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596685318\">To find a third solution, we\u2019ll let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/> and solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<p><span id=\"fs-id1169596685335\" data-type=\"media\" data-alt=\"The figure shows the steps to solve for y when x equals 2 in the equation y equals 5 x minus 1. The equation y equals 5 x minus 1 is shown. Below it is the equation with 2 substituted in for x which is y equals 5 times 2 minus 1. To solve for y first multiply so that the equation becomes y equals 10 minus 1 then subtract so that the equation is y equals 9.\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_040_img_new.jpg\" alt=\"The figure shows the steps to solve for y when x equals 2 in the equation y equals 5 x minus 1. The equation y equals 5 x minus 1 is shown. Below it is the equation with 2 substituted in for x which is y equals 5 times 2 minus 1. To solve for y first multiply so that the equation becomes y equals 10 minus 1 then subtract so that the equation is y equals 9.\" width=\"242\" height=\"112\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594160564\">The ordered pair <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aed69bebaba922065b21b4b0c0decd0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> is a solution to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e97f6bd16e4dfbf96ffc41bc5250fd2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/>. We will add it to <a class=\"autogenerated-content\" href=\"#fs-id1169594160564\">(Table 2)<\/a>.<\/p>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 406px;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e97f6bd16e4dfbf96ffc41bc5250fd2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/strong><\/span><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 76.3438px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/span><\/td>\n<td style=\"width: 84.375px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/span><\/td>\n<td style=\"width: 248px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 76.3438px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">0<\/span><\/td>\n<td style=\"width: 84.375px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/span><\/td>\n<td style=\"width: 248px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ec6084fa217f87f8fc5df481ca60ccf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 76.3438px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">1<\/span><\/td>\n<td style=\"width: 84.375px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\">4<\/span><\/td>\n<td style=\"width: 248px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><span style=\"background-color: #ffffff; color: #000000;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ab73a57c5e039ffb22ed1a8e29747bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 76.3438px; text-align: center;\"><span style=\"background-color: #ffffff; color: #000000;\">2<\/span><\/td>\n<td style=\"width: 84.375px; text-align: center;\"><span style=\"background-color: #ffffff; color: #000000;\">9<\/span><\/td>\n<td style=\"width: 248px; text-align: center;\"><span style=\"background-color: #ffffff; color: #000000;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aed69bebaba922065b21b4b0c0decd0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596435756\">We can find more solutions to the equation by substituting in any value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> or any value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> and solving the resulting equation to get another ordered pair that is a solution. There are infinitely many solutions of this equation.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596437443\" style=\"text-align: center;\" data-type=\"problem\">\n<p id=\"fs-id1169596437445\">Complete the table\u00a0to find three solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d76269f8d9b324873c9b8e3993ef6892_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 406px;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d76269f8d9b324873c9b8e3993ef6892_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">2<\/td>\n<td style=\"width: 81.4062px; text-align: center;\"><\/td>\n<td style=\"width: 240.406px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<div id=\"fs-id1169596388103\" style=\"text-align: center;\" data-type=\"solution\">\n<div style=\"text-align: left;\" data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596253289\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ad143a0d979362a51b48a48c9ca9f59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c657687cbbf5ea9a7545edb42190e592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/> into <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d76269f8d9b324873c9b8e3993ef6892_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/>.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_036_img_new.jpg\" alt=\"This figure has three columns. At the top of the first column is the value x equals 0. Below this is the equation y equals 4x minus 2. Below this is the same equation with 0 substituted for x: y equals 4 times 0 minus 2. Below this is y equals 0 minus 2. Below this is y equals negative 2. Below this is the ordered pair (0, negative 2). At the top of the second column is the value x equals negative 1. Below this is the equation y equals 4x minus 2. Below this is the same equation with negative 1 substituted for x: y equals 4 times minus 1 minus 2. Below this is y equals negative 4 minus 2. Below this is y equals negative 6. Below this is the ordered pair (negative 1, negative 6). At the top of the third column is the value x equals 2. Below this is the equation y equals 4x minus 2. Below this is the same equation with 2 substituted for x: y equals 4 times 2 minus 2. Below this is y equals 8 minus 2. Below this is y equals 6. Below this is the ordered pair (2, 6).\" data-media-type=\"image\/jpeg\" \/><\/p>\n<p id=\"fs-id1169594087041\">The results are summarized in the table below.<\/p>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d76269f8d9b324873c9b8e3993ef6892_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ecef9f206503704c74407265b403ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-379fdae439000a3929a84b18bd04fcb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">2<\/td>\n<td style=\"width: 81.4062px; text-align: center;\">\u00a0 6<\/td>\n<td style=\"width: 240.406px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-80be894898c77ffda9d4d5843e6791f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596764393\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596764397\" data-type=\"exercise\">\n<div id=\"fs-id1169596764399\" data-type=\"problem\">\n<p id=\"fs-id1169596764401\">Complete the table to find three solutions to this equation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-09acfc77aa1f355947c21a5c0e345588_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-09acfc77aa1f355947c21a5c0e345588_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">2<\/td>\n<td style=\"width: 81.4062px; text-align: center;\"><\/td>\n<td style=\"width: 240.406px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-09acfc77aa1f355947c21a5c0e345588_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#51;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ec6084fa217f87f8fc5df481ca60ccf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8235f4c83db17d3a3454713a44752b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">2<\/td>\n<td style=\"width: 81.4062px; text-align: center;\">5<\/td>\n<td style=\"width: 240.406px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2da1eb750fc283f55cb9396d5536b47a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169594211909\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594211913\" data-type=\"exercise\">\n<div id=\"fs-id1169594105663\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596253005\" data-type=\"problem\">\n<p id=\"fs-id1169596253007\">Complete the table to find three solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8ffcdec806bdcfb54d462afc156b6a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#52;&#121;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8ffcdec806bdcfb54d462afc156b6a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#52;&#121;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\"><\/td>\n<td style=\"width: 81.4062px; text-align: center;\">5<\/td>\n<td style=\"width: 240.406px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1169596421536\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169594243050\">Substitute the given value into the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8ffcdec806bdcfb54d462afc156b6a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#52;&#121;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/> and solve for the other variable. Then, fill in the values in the table.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-id1169594243073\" data-type=\"media\" data-alt=\"This figure has three columns. At the top of the first column is the value x equals 0. Below this is the equation 5x minus 4y equals 20. Below this is the same equation with 0 substituted for x: 5 times 0 minus 4y equals 20. Below this is 0 minus 4y equals 20. Below this is negative 4y equals 20. Below this is y equals negative 5. Below this is the ordered pair (0, negative 5). At the top of the second column is the value y equals 0. Below this is the equation 5x minus 4y equals 20. Below this is the same equation with 0 substituted for y: 5x minus 4 times 0 equals 20. Below this is 5x minus 0 equals 20. Below this is 5x equals 20. Below this is x equals 4. Below this is the ordered pair (4, 0). At the top of the third column is the value y equals 5. Below this is the equation 5x minus 47 equals 20. Below this is the same equation with 5 substituted for y: 5x minus 4 times 5 equals 20. Below this is the equation 5x minus 20 equals 20. Below this is 5x equals 40. Below this is x equals 8. Below this is the ordered pair (8, 5).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_037_img_new.jpg\" alt=\"This figure has three columns. At the top of the first column is the value x equals 0. Below this is the equation 5x minus 4y equals 20. Below this is the same equation with 0 substituted for x: 5 times 0 minus 4y equals 20. Below this is 0 minus 4y equals 20. Below this is negative 4y equals 20. Below this is y equals negative 5. Below this is the ordered pair (0, negative 5). At the top of the second column is the value y equals 0. Below this is the equation 5x minus 4y equals 20. Below this is the same equation with 0 substituted for y: 5x minus 4 times 0 equals 20. Below this is 5x minus 0 equals 20. Below this is 5x equals 20. Below this is x equals 4. Below this is the ordered pair (4, 0). At the top of the third column is the value y equals 5. Below this is the equation 5x minus 47 equals 20. Below this is the same equation with 5 substituted for y: 5x minus 4 times 5 equals 20. Below this is the equation 5x minus 20 equals 20. Below this is 5x equals 40. Below this is x equals 8. Below this is the ordered pair (8, 5).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169594243093\">The results are summarized in the table below.<\/p>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8ffcdec806bdcfb54d462afc156b6a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#52;&#121;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.2812px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 81.2969px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 240.844px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.2812px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.2969px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 240.844px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5f6ab1a0ed415088c10eaaa3977a4992_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.2812px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td style=\"width: 81.2969px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 240.844px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2809647061e2f05aa3080110836f8805_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.2812px; text-align: center;\">8<\/td>\n<td style=\"width: 81.2969px; text-align: center;\">5<\/td>\n<td style=\"width: 240.844px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-648acaf5866f6160ec660bee40426678_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596684659\" class=\"bc-section section\" data-depth=\"1\">\n<div id=\"fs-id1169596243950\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596243954\" data-type=\"exercise\">\n<div id=\"fs-id1169596243956\" data-type=\"problem\">\n<p id=\"fs-id1169596243958\">Complete the table to find three solutions to this equation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ba683d43e8125b744e87d8d53eae736_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#53;&#121;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ba683d43e8125b744e87d8d53eae736_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#53;&#121;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 81.4062px; text-align: center;\"><\/td>\n<td style=\"width: 240.406px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div id=\"fs-id1169596446946\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ba683d43e8125b744e87d8d53eae736_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#53;&#121;&#61;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-42f3c0bd5adc0ec0fa1707d7989e5c00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">10<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d5c4757cfffcea3882a6dda84d2b0d19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 81.4062px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 240.406px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bb202e0826326eae1d4751969417d175_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find Solutions to a Linear Equation<\/h1>\n<p id=\"fs-id1169594031699\">To find a solution to a linear equation, you really can pick <em data-effect=\"italics\">any<\/em> number you want to substitute into the equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-62f853fa6f372493298c507883a9f490_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\" \/> But since you\u2019ll need to use that number to solve for the other variable it\u2019s a good idea to choose a number that\u2019s easy to work with.<\/p>\n<p id=\"fs-id1169596368122\">When the equation is in <em data-effect=\"italics\">y<\/em>-form, with the <em data-effect=\"italics\">y<\/em> by itself on one side of the equation, it is usually easier to choose values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and then solve for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Find three solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fc90afade1fa88a952541d19de3fa12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<div id=\"fs-id1169596368171\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596439896\">We can substitute any value we want for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> or any value for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>. Since the equation is in <em data-effect=\"italics\">y<\/em>-form, it will be easier to substitute in values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/>. Let\u2019s pick <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3330a01aa4d7d81947b71297d8623d3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: -1px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ad143a0d979362a51b48a48c9ca9f59e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: -1px;\" \/>.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<table id=\"eip-id1172184886219\" style=\"height: 172px; width: 100%;\" summary=\"This figure contains three columns. The leftmost column contains step-by-step instructions for finding ordered pairs that are solutions to the equation y equals negative 3x plus 2. These steps are: \u201cSubstitute the value into the equation,\u201d \u201cSimplify\u201d, \u201cSolve,\u201d \u201cWrite the ordered pair,\u201d and \u201cCheck.\u201d At the top of the second column is the value x equals 0. Below this is the equation y equals negative 3x plus 2. Below this is the equation with 0 substituted for x: y equals negative 3 times 0 plus 2. Below this is the equation simplified: y equals 0 plus 2. Below this is the equation solved: y equals 2. Below this is the ordered pair (0, 2). Below this is the equation y equals negative 3x plus 2 again. Below this is the equation with 0 and 2 substituted for x and y, ready to be checked: 2 might equal negative 3 times 0 plus 2. Below this is 2 might equal 0 plus 2. Below this is 2 equals 2, with a check mark next to it. At the top of the third column is the value x equals 1. Below this is the equation y equals negative 3x plus 2. Below this is the equation with 1 substituted for x: y equals negative 3 times 1 plus 2. Below this is the equation simplified: y equals negative 3 plus 2. Below this is the equation solved: y equals negative 1. Below this is the ordered pair (1, negative 1). Below this is the equation y equals negative 3x plus 2 again. Below this is the equation with 1 and negative 1 substituted for x and y, ready to be checked: negative 1 might equal negative 3 times 1 plus 2. Below this is negative 1 might equal negative 3 plus 2. Below this is negative 1 equals negative 1, with a check mark next to it. At the top of the fourth column is the value x equals negative 1. Below this is the equation y equals negative 3x plus 2. Below this is the equation with negative 1 substituted for x: y equals negative 3 times negative 1 plus 2. Below this is the equation simplified: y equals 3 plus 2. Below this is the equation solved: y equals 5. Below this is the ordered pair (negative 1, 5). Below this is the equation y equals negative 3x plus 2 again. Below this is the equation with negative 1 and 5 substituted for x and y, ready to be checked: 5 might equal negative 3 times negative 1 plus 2. Below this is 5 might equal 3 plus 2. Below this is 5 equals 5, with a check mark next to it.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\"><\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><span id=\"eip-id1172188157425\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><span id=\"eip-id1172188157435\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><span id=\"eip-id1172188157445\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\">Substitute the value into the equation.<\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><span id=\"eip-id1172181443943\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><span id=\"eip-id1172181443953\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><span id=\"eip-id1172181443964\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\">Simplify.<\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><span id=\"eip-id1172181443980\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><span id=\"eip-id1172183445895\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><span id=\"eip-id1172183445905\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\">Simplify.<\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><span id=\"eip-id1172183445922\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><span id=\"eip-id1172183445932\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><span id=\"eip-id1172183445942\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038n_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\">Write the ordered pair.<\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><span id=\"eip-id1172184380866\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><span id=\"eip-id1172184380876\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><span id=\"eip-id1172184380887\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_038o_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\">Check.<\/td>\n<td style=\"width: 24.2045%; height: 14px;\">(0, 2)<\/td>\n<td style=\"width: 21.8182%; height: 14px;\">(1, \u22121)<\/td>\n<td style=\"width: 23.9772%; height: 14px;\">(\u22121, 5)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\"><\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fc90afade1fa88a952541d19de3fa12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fc90afade1fa88a952541d19de3fa12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fc90afade1fa88a952541d19de3fa12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 29.9183%; height: 30px;\" colspan=\"3\"><\/td>\n<td style=\"width: 24.2045%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b3472dd1159463c3f02002a7c3ccf6cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#45;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"106\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 21.8182%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3b853f3e85446021dfc913b6c0ded676_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#45;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 23.9772%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c135bf368e4d0040b12a34ae04f34abf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px;\">\n<td style=\"width: 29.9183%; height: 30px;\" colspan=\"3\"><\/td>\n<td style=\"width: 24.2045%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-283a6d4afe512d41fb4796659503bf1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#48;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"71\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 21.8182%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cdd86ffc766c91dc61db3e0677c0e61f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#45;&#51;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"98\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 23.9772%; height: 30px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3affcd2874e56e89fec40c39c6c8c04b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#51;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"71\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 29.9183%; height: 14px;\" colspan=\"3\"><\/td>\n<td style=\"width: 24.2045%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-a01cddcf4b7507739275accc6d31f36c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#61;&#50;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 21.8182%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-683d08a493a8fc40b05a11e624b4ae1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#61;&#45;&#49;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"82\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 23.9772%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fc464fd146c46bf24196e4d22658dee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#61;&#53;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169596387161\">So, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-398828550549fdd4b2191f8f7cde7bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c3ac38dbb39343c28a60a287dfb114b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1c6cf6f67551105173d9fb3cab5966cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/> are all solutions to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fc90afade1fa88a952541d19de3fa12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/>. We show them in table below.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4fc90afade1fa88a952541d19de3fa12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#51;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-398828550549fdd4b2191f8f7cde7bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c3ac38dbb39343c28a60a287dfb114b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 81.4062px; text-align: center;\">5<\/td>\n<td style=\"width: 240.406px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1c6cf6f67551105173d9fb3cab5966cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596756232\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596756237\" data-type=\"exercise\">\n<div id=\"fs-id1169596756239\" data-type=\"problem\">\n<p id=\"fs-id1169596756241\">Find three solutions to this equation: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d1307bebf3c96fca8778786c5d15082d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594028678\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594028680\">Answers will vary.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169594028723\">We have seen how using zero as one value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> makes finding the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> easy. When an equation is in standard form, with both the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> on the same side of the equation, it is usually easier to first find one solution when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> find a second solution when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>, and then find a third solution.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594029355\" data-type=\"problem\">\n<p id=\"fs-id1169594029357\">Find three solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596435800\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1169596435805\">We can substitute any value we want for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> or any value for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/>. Since the equation is in standard form, let\u2019s pick first <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-8203ced39e0cdafefa708857c7ec2264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/>, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5e8ef70615fdaee8588017ac1fdd2da0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/>, and then find a third point.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<table id=\"eip-id1172182678898\" style=\"width: 100%; height: 469px;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\"><\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172189391855\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172187698025\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039g_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172187698035\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039m_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\"><\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172187698051\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172187181962\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039h_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172187181972\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039n_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\">Substitute the value into the equation.<\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172182567983\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172182567994\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039i_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172182568004\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039o_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\">Simplify.<\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172185549081\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172185549090\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039j_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172185549100\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039p_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\">Solve.<\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172189367366\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172189367377\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039k_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172182380250\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039q_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\"><\/td>\n<td style=\"width: 153.406px;\"><span id=\"eip-id1172182380265\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039f_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 139.406px;\"><span id=\"eip-id1172182380276\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039l_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td style=\"width: 126.406px;\"><span id=\"eip-id1172187646915\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_039r_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\">Write the ordered pair.<\/td>\n<td style=\"width: 153.406px;\" data-align=\"right\">(0, 3)<\/td>\n<td style=\"width: 139.406px;\" data-align=\"right\">(2, 0)<\/td>\n<td style=\"width: 126.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bcfb46537bc87e905a152e0aeb5f6d71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"50\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 198.406px;\" colspan=\"3\">Check.<\/td>\n<td style=\"width: 153.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 139.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 126.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.4062px;\" colspan=\"3\" data-align=\"right\"><\/td>\n<td style=\"width: 153.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e4b0481b094c308827b3de6ad4e6de08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#43;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"115\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 139.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-324d2945b6f4adafcc174043cf70080c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#43;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"115\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 126.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ebea92fa368e17d93bb5a1960f6764b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#43;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"117\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.4062px;\" colspan=\"3\" data-align=\"right\"><\/td>\n<td style=\"width: 153.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bc98f3506920ac74dfe22549bb624320_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#43;&#54;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"72\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 139.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-fe085678b14ef90a0240dfdfc5008ce8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#43;&#48;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"72\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 126.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c38611642766e2b52f5266db5ea57dab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#51;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#63;&#125;&#123;&#61;&#125;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"72\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 69.4062px;\" colspan=\"3\" data-align=\"right\"><\/td>\n<td style=\"width: 153.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-84adab1b32b0263f783d2f6c0f50502a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#61;&#54;&#92;&#99;&#104;&#101;&#99;&#107;&#109;&#97;&#114;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 139.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0298acbe2fe9de051d91f10512dc1874_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#61;&#54;&#10003;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 126.406px;\" data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0298acbe2fe9de051d91f10512dc1874_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#61;&#54;&#10003;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169594079033\">So <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ef24d382319a3ce81f280194edba003a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-559928bd7c8949c8342dd73437aef05a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-bcfb46537bc87e905a152e0aeb5f6d71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"50\" style=\"vertical-align: -17px;\" \/> are all solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>. We can list these three solutions in the table below.<span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<table id=\"fs-id1169594029160\" class=\"aligncenter\" style=\"width: 100%;\" summary=\"The top row of this table, which is a header row, contains the equation y equals 5x minus 1. The second row, which is also a header row, is split into three columns. Each cell in this row names the column below it. The first cell is labeled \u201cx\u201d, the second cell is labeled \u201cy\u201d, and the third column is labeled with the ordered pair (x, y). In the third row, the x column contains 0, the y column contains negative 1, and the (x, y) column contains the ordered pair (0, negative 1). In the fourth row, the x column contains 1, the y column contains 4, and the (x, y) column contains the ordered pair (1, 4).\">\n<caption><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-11dc2d3604131c2e789dafb672c0914b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/strong><\/caption>\n<tbody>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ef24d382319a3ce81f280194edba003a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px;\" valign=\"top\">\n<td style=\"width: 73.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td style=\"width: 81.4062px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td style=\"width: 240.406px; height: 16px; text-align: center;\" data-valign=\"middle\" data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-559928bd7c8949c8342dd73437aef05a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 73.4062px; text-align: center;\">1<\/td>\n<td style=\"width: 81.4062px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6d841d87b9a5793727b0590b3272eb6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\" \/><\/td>\n<td style=\"width: 240.406px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-88f2263d8651fd90555f6b8379151082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"40\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169594031694\" class=\"bc-section section\" data-depth=\"1\">\n<div id=\"fs-id1169594025622\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169594025626\" data-type=\"exercise\">\n<div id=\"fs-id1169594025628\" data-type=\"problem\">\n<p id=\"fs-id1169594025630\">Find three solutions to the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-07795f3421886c79416fa26cd22cc5f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169594025652\" data-type=\"solution\">\n<details>\n<summary class=\"answer\">Show answer<\/summary>\n<p id=\"fs-id1169594025654\">Answers will vary.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1169594122360\">\n<dt>linear equation<\/dt>\n<dd id=\"fs-id1169594122365\">A linear equation is of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0520a31036e9a951aea74693c8b23cb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#120;&#43;&#66;&#121;&#61;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"106\" style=\"vertical-align: -4px;\" \/>, where A and B are not both zero, is called a linear equation in two variables.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594122387\">\n<dt>ordered pair<\/dt>\n<dd id=\"fs-id1169594122393\">An ordered pair <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/> gives the coordinates of a point in a rectangular coordinate system.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594122415\">\n<dt>origin<\/dt>\n<dd id=\"fs-id1169594122420\">The point <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/> is called the origin. It is the point where the <em data-effect=\"italics\">x<\/em>-axis and <em data-effect=\"italics\">y<\/em>-axis intersect.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594132646\">\n<dt>quadrant<\/dt>\n<dd id=\"fs-id1169594132651\">The <em data-effect=\"italics\">x<\/em>-axis and the <em data-effect=\"italics\">y<\/em>-axis divide a plane into four regions, called quadrants.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594132666\">\n<dt>rectangular coordinate system<\/dt>\n<dd id=\"fs-id1169594132671\">A grid system is used in algebra to show a relationship between two variables; also called the <em data-effect=\"italics\">xy<\/em>-plane or the \u2018coordinate plane.\u2019<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594132682\">\n<dt><em data-effect=\"italics\">x<\/em>-coordinate<\/dt>\n<dd id=\"fs-id1169594132691\">The first number in an ordered pair <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/>.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169594132713\">\n<dt><em data-effect=\"italics\">y<\/em>-coordinate<\/dt>\n<dd id=\"fs-id1169594132723\">The second number in an ordered pair <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/>.<\/dd>\n<\/dl>\n<\/div>\n<h1>3.1 Exercise Set.<\/h1>\n<p id=\"fs-id1169595541833\">In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.<\/p>\n<ol class=\"twocolumn\">\n<li>\n<ol type=\"A\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ad41549099069a514e17dfbc399b6c68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ce38ace23dd1b8f15095a1aff4a73f36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-afaa85d80f816c5a4c4a30f7848f7f78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5aa29da239e6fed61429835a4b4444af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-64d8120241193ac47be39d83562a0dd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#51;&#125;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"40\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"A\">\n<li><span data-type=\"newline\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0d66a71b8940b998e4f29f8cccda06d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/span><\/li>\n<li><span data-type=\"newline\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0e0819cfb987fa92d333add15bb2e864_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/span><\/li>\n<li><span data-type=\"newline\"> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-627391f2fad7216057fc57692a374893_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/span><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e2c3a69d33f9737210f9c4f1551f4b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><span data-type=\"newline\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b306914c9166160cb903d32a58e7a3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"47\" style=\"vertical-align: -7px;\" \/><\/span><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p id=\"fs-id1169594082455\">In the following exercises, plot each point in a rectangular coordinate system.<\/p>\n<ol class=\"twocolumn\" start=\"3\">\n<li>\n<ol type=\"A\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dd6f8f312ab67ad0422a4959540654f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7ba9cc2a7f12e65a6b3de8f34bcc16e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5aa29da239e6fed61429835a4b4444af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-398828550549fdd4b2191f8f7cde7bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li>\n<ol type=\"A\">\n<li><span data-type=\"newline\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c53627fd7039dcb62c54d86fe468e6e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/span><\/li>\n<li><span data-type=\"newline\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-017f20ea0c6fda3470cedb20ea0b5537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/span><\/li>\n<li><span data-type=\"newline\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-91357ad9f837f690ca370a0ee126647e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/span><\/li>\n<li><span data-type=\"newline\"> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d6c757b148db3a6707e7e1f199d80f9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/span><\/li>\n<li><span data-type=\"newline\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ecef9f206503704c74407265b403ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/span><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p id=\"fs-id1169594008366\">In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.<\/p>\n<table class=\"no-lines\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">5.<\/p>\n<div id=\"fs-id1169594008370\" class=\"material-set-2\" data-type=\"exercise\">\n<div id=\"fs-id1169594008372\" data-type=\"problem\"><span id=\"fs-id1169594008378\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 4, 1) is plotted and labeled \u201cA\u201d. The point (negative 3, negative 4) is plotted and labeled \u201cB\u201d. The point (1, negative 3) is plotted and labeled \u201cC\u201d. The point (4, 3) is plotted and labeled \u201cD\u201d.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_209_img_new.jpg\" alt=\"A graph plotting the points A (negative 4, 1), B (negative 3, negative 4), C (1, negative 3), D (4, 3).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/div>\n<\/td>\n<td style=\"width: 50%;\">\n<div id=\"fs-id1169594041705\" class=\"material-set-2\" data-type=\"exercise\">\n<div data-type=\"problem\">6.<\/div>\n<\/div>\n<div id=\"fs-id1169594176002\" class=\"material-set-2\" data-type=\"exercise\">\n<div id=\"fs-id1169594176004\" data-type=\"problem\"><span id=\"fs-id1169594176010\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (0, negative 2) is plotted and labeled \u201cA\u201d. The point (negative 2, 0) is plotted and labeled \u201cB\u201d. The point (0, 5) is plotted and labeled \u201cC\u201d. The point (5, 0) is plotted and labeled \u201cD\u201d.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_211_img_new.jpg\" alt=\"A graph plotting the points A (0, negative 2), B (negative 2, 0), C (0, 5), D (5, 0).\" width=\"301\" height=\"309\" data-media-type=\"image\/jpeg\" \/><\/span><\/div>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169595582756\">In the following exercises, which ordered pairs are solutions to the given equations?<\/p>\n<ol class=\"twocolumn\" start=\"7\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-916cc1be8cd05a1ae6eeaf20edae6017_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/>\n<ol type=\"A\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ab73a57c5e039ffb22ed1a8e29747bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-28a186f2424d2e935d6aa6388441b6d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3fca1a384cf5042876a719066cbbb127_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3dab7a056e3ac248ffb470282b1b70af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#50;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/>\n<ol type=\"A\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f3b8ee106f7e5a95f1dd3e0ab5f16435_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ab73a57c5e039ffb22ed1a8e29747bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-42f3c0bd5adc0ec0fa1707d7989e5c00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-88a9e1e61a2f782c82ce1508f5c76c40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/>\n<ol type=\"A\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b1804935101b0791adf13cb00d6ac306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7a98d0e71a22be78d161caf964026b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b8d0fd073a3c363608af97ce56ad9bb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"40\" style=\"vertical-align: -7px;\" \/><\/li>\n<\/ol>\n<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0df0502aa6d0215343d5a7714e47c282_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/>\n<ol type=\"A\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-559928bd7c8949c8342dd73437aef05a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c0ebfefe0e9cb3e7577fd49b23632fa0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4ef6c187a0599fedf1caa75800c24233_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div id=\"fs-id1169596379766\" class=\"practice-perfect\" data-depth=\"2\">\n<p id=\"fs-id1169595272384\">In the following exercises, complete the table to find solutions to each linear equation.<\/p>\n<table class=\"no-lines\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 49.3711%;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-849b10efbe1af148e921ad81488f9a23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#50;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 49.3711%;\">\n<p id=\"fs-id1169596635797\">\u00a012. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0e11a0299f0d468a4bcdb176a3f9deee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 49.3711%;\">\n<div id=\"fs-id1169596635792\" data-type=\"exercise\">\n<div data-type=\"problem\"><\/div>\n<\/div>\n<div data-type=\"exercise\">\u00a013. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-07df8bb2e7964213c71becbdf5b0c19b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -6px;\" \/><\/div>\n<div id=\"fs-id1169594176646\" data-type=\"exercise\">\n<div id=\"fs-id1169594176648\" data-type=\"problem\">\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">6<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/td>\n<td style=\"width: 49.3711%;\">\n<p id=\"fs-id1169594105772\">\u00a014. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-33bb545c6023a713ac9c20aacbc8cb50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#125;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"97\" style=\"vertical-align: -6px;\" \/><\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr style=\"height: 196px;\">\n<td style=\"width: 49.3711%; height: 196px;\">\n<p id=\"fs-id1169594031127\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-5488c11d94bab4f4665a6fed9f837a47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#51;&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 49.3711%; height: 196px;\">\n<div id=\"fs-id1169596755278\" data-type=\"problem\">\n<p>16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-2c22eccd4d2611409a3b750d352d2d54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#53;&#121;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"problem\">\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">10<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1169596647833\" data-type=\"exercise\">\n<div id=\"fs-id1169596647835\" data-type=\"problem\"><span style=\"orphans: 1; text-align: initial; font-size: 14pt;\">In the following exercises, find three solutions to each linear equation.<\/span><\/div>\n<ol class=\"twocolumn\" start=\"17\">\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-47ec1d9e571b6cdf494b31f8ef9b0a59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#120;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-13b7d4f55a34a340eb49d4a59cdd9d12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f4de53d0e38dd08e248571e9120e59e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-25f0cd4a1ebf42794184f8902f6fca30_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f5e5d8d536bd15610418e85b413562ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6cb7584b6cb0af341c1c860d92c901d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0b4975bc970086d0340ab18bc591d220_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#52;&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/li>\n<li data-type=\"problem\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6164c043070e69d3aa4a01df3d43e126_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#50;&#121;&#61;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<table class=\"no-lines\" style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1169594006211\"><strong data-effect=\"bold\">25. <\/strong>\u00a0Mackenzie recorded her baby\u2019s weight every two months. The baby\u2019s age, in months, and weight, in pounds, are listed in the table below, and shown as an ordered pair in the third column.<\/p>\n<p id=\"fs-id1169594006220\"><span class=\"token\">a)<\/span>\u00a0Plot the points on a coordinate plane.<\/p>\n<p><span id=\"fs-id1171784026239\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_216_img_new.jpg\" alt=\"The x y axis with no points plotted.\" width=\"176\" height=\"160\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1171784026251\"><span class=\"token\">b)<\/span> Why is only Quadrant I needed?<\/p>\n<table id=\"fs-id1169594006239\" class=\"grid\" summary=\"This table has three columns. The top row is a header row, and each cell names the column below it. From left to right, the first column is labeled \u201cAge, x\u201d, the second column is labeled \u201cWeight, y\u201d, and the third column is labeled with the ordered pair (x, y). In the second row, the \u201cAge\u201d column contains 0, the \u201cWeight\u201d column contains 7, and the (x, y) column contains the ordered pair (0, 7). In the third row, the \u201cAge\u201d column contains 2, the \u201cWeight\u201d column contains 11, and the (x, y) column contains the ordered pair (0, 7). In the fourth row, the \u201cAge\u201d column contains 4, the \u201cWeight\u201d column contains 14, and the (x, y) column contains the ordered pair (4, 15). In the fifth row, the \u201cAge\u201d column contains 6, the \u201cWeight\u201d column contains 16, and the (x, y) column contains the ordered pair (6, 16). In the sixth row, the \u201cAge\u201d column contains 8, the \u201cWeight\u201d column contains 19, and the (x, y) column contains the ordered pair (8, 19). In the seventh row, the \u201cAge\u201d column contains 10, the \u201cWeight\u201d column contains 20, and the (x, y) column contains the ordered pair (10, 20). In the eighth row, the \u201cAge\u201d column contains 12, the \u201cWeight\u201d column contains 21, and the (x, y) column contains the ordered pair (12, 21).\">\n<tbody>\n<tr valign=\"top\">\n<th scope=\"col\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">Age <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/th>\n<th scope=\"col\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\">Weight <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/th>\n<th scope=\"col\" data-valign=\"bottom\" data-align=\"center\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/th>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">7<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(0, 7)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">11<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(2, 11)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">15<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(4, 15)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">6<\/td>\n<td data-valign=\"middle\" data-align=\"center\">16<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(6, 16)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">8<\/td>\n<td data-valign=\"middle\" data-align=\"center\">19<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(8, 19)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">10<\/td>\n<td data-valign=\"middle\" data-align=\"center\">20<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(10, 20)<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"center\">12<\/td>\n<td data-valign=\"middle\" data-align=\"center\">21<\/td>\n<td data-valign=\"middle\" data-align=\"center\">(12, 21)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1.<\/p>\n<p><span id=\"fs-id1169594030981\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 4, 2) is plotted and labeled &quot;a&quot;. The point (negative 1, negative 2) is plotted and labeled &quot;b&quot;. The point (3, negative 5) is plotted and labeled &quot;c&quot;. The point (negative 3, 5) is plotted and labeled \u201cd\u201d. The point (5 thirds, 2) is plotted and labeled \u201ce\u201d.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_201_img_new.jpg\" alt=\"A graph plotting the points a (negative 4, 2), b (negative 1, negative 2), c (3, negative 5), d (negative 3, 5), e (5 thirds, 2).\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\" \/>\u00a0<\/span><\/td>\n<td style=\"width: 50%;\">2.<\/p>\n<p><span id=\"fs-id1169594034148\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (3, negative 1) is plotted and labeled &quot;a&quot;. The point (negative 3, 1) is plotted and labeled &quot;b&quot;. The point (negative 2, 2) is plotted and labeled &quot;c&quot;. The point (negative 4, negative 3) is plotted and labeled \u201cd\u201d. The point (1, 14 fifths) is plotted and labeled \u201ce\u201d.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_203_img_new.jpg\" alt=\"A graph plotting the points a (3, negative 1), b (negative 3, 1), c (negative 2, 2), d (negative 4, negative 3), e (1, 14 fifths).\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3.<\/p>\n<p><span id=\"fs-id1169596767368\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (negative 2, 0) is plotted and labeled &quot;a&quot;. The point (negative 3, 0) is plotted and labeled &quot;b&quot;. The point (0, 0) is plotted and labeled &quot;c&quot;. The point (0, 4) is plotted and labeled \u201cd\u201d. The point (0, 3) is plotted and labeled \u201ce\u201d.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_205_img_new.jpg\" alt=\"A graph plotting the points a (negative 2, 0), b (negative 3, 0), c (0, 0), d (0, 4), e (0, 3).\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%;\">4.<\/p>\n<p><span id=\"fs-id1169594031347\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (0, 0) is plotted and labeled &quot;a&quot;. The point (0, negative 3) is plotted and labeled &quot;b&quot;. The point (negative 4, 0) is plotted and labeled &quot;c&quot;. The point (1, 0) is plotted and labeled \u201cd\u201d. The point (0, negative 2) is plotted and labeled \u201ce\u201d.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_207_img_new.jpg\" alt=\"A graph plotting the points a (0, 0), b (0, negative 3), c (negative 4, 0), d (1, 0), e (0, negative 2).\" width=\"217\" height=\"224\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol class=\"twocolumn\" start=\"5\">\n<li>A: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-cba4706a21fad1e77985563696d1bdae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>\u2003B: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-9523da542e5bfc81814e047c926984c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/>\u2003C: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-876cb3caf33e984a34d443f2b79f105e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#44;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>\u2003D: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-b1804935101b0791adf13cb00d6ac306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>A: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ecef9f206503704c74407265b403ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/>\u2003B: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-dd6f8f312ab67ad0422a4959540654f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/>\u2003C: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6655aef23bcf82d48b1ff5bf888d5b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/>\u2003D: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e3e1928d65786877c787a2d401d9e77e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/li>\n<li>A, B<\/li>\n<li>A, C<\/li>\n<li>B, C<\/li>\n<li>A, B<\/li>\n<\/ol>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">11.<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 62px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-42f3c0bd5adc0ec0fa1707d7989e5c00_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 20px; text-align: center;\">2<\/td>\n<td style=\"width: 14.1766%; height: 20px; text-align: center;\">0<\/td>\n<td style=\"width: 11.8073%; height: 20px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-559928bd7c8949c8342dd73437aef05a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b34c01098c83fa602de54e9d74d63a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4797c874a138ca175d7c2cd8b3ed9a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-379fdae439000a3929a84b18bd04fcb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#44;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">12.<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 66px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">5<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-6655aef23bcf82d48b1ff5bf888d5b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 24px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 24px; text-align: center;\">2<\/td>\n<td style=\"width: 11.8073%; height: 24px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f3b8ee106f7e5a95f1dd3e0ab5f16435_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">7<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-374b47fb7bf10f554c21530f0ecc88e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">13.<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">1<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-99d11505e9b59f8e2d3351529e3354c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-f3b8ee106f7e5a95f1dd3e0ab5f16435_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">6<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-1f1a235ff31c373d5cda1965ad172871_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">14.<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ecef9f206503704c74407265b403ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-c02ba61efe13be423bc75f83a9846930_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#44;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">1<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e86393e45c0f6cf9bb7fcf130d3db9da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"51\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">15.<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-398828550549fdd4b2191f8f7cde7bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">3<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">4<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-4307e3633578c7e56f8f767895b20497_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#44;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">6<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-d7121f8d5dd68d2f78cd8dd11d35a5dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<td style=\"width: 33.3333%; height: 15px;\">16.<\/p>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 50%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/><\/strong><\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><strong data-effect=\"bold\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-aee61752ae042431152087f74b766103_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#44;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-17c33e2329e29a62a80ad2b547b4753d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-3ecef9f206503704c74407265b403ee3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#44;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">10<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">2<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-62c84bb2f701cca07b15dd383edaae7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#44;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"47\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 11.5261%; height: 14px; text-align: center;\">5<\/td>\n<td style=\"width: 14.1766%; height: 14px; text-align: center;\">0<\/td>\n<td style=\"width: 11.8073%; height: 14px; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-content\/ql-cache\/quicklatex.com-e3e1928d65786877c787a2d401d9e77e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#44;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol class=\"twocolumn\" start=\"17\">\n<li>Answers will vary.<\/li>\n<li>Answers will vary.<\/li>\n<li>Answers will vary.<\/li>\n<li>Answers will vary.<\/li>\n<li>Answers will vary.<\/li>\n<li>Answers will vary.<\/li>\n<li>Answers will vary.<\/li>\n<li>Answers will vary.<\/li>\n<\/ol>\n<table class=\"grid\" style=\"border-collapse: collapse; width: 100%; height: 306px;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\">25.<\/p>\n<p id=\"fs-id1169594249629\"><span class=\"token\">a)<\/span><span data-type=\"newline\"><br \/>\n<\/span><\/p>\n<p><span id=\"fs-id1169594249634\" data-type=\"media\" data-alt=\"The graph shows the x y-coordinate plane. The x- and y-axes each run from 0 to 25. The points (0, 7), (2, 11), (4, 15), (6, 16), (8, 19), (10, 20) and (12, 21) are plotted and labeled.\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/opentextbc.ca\/oerdiscipline\/wp-content\/uploads\/sites\/361\/2021\/08\/CNX_ElemAlg_Figure_04_01_213_img_new.jpg\" alt=\"A graph that plots the points (0, 7), (2, 11), (4, 15), (6, 16), (8, 19), (10, 20) and (12, 21).\" width=\"176\" height=\"160\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p><span class=\"token\">b)<\/span> Age and weight are only positive.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cUse the Rectangular Coordinate System\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Adaptation Statement for more information.<\/p>\n","protected":false},"author":125,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-836","chapter","type-chapter","status-publish","hentry"],"part":777,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/836","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/users\/125"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/836\/revisions"}],"predecessor-version":[{"id":837,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/836\/revisions\/837"}],"part":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/parts\/777"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapters\/836\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/media?parent=836"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/pressbooks\/v2\/chapter-type?post=836"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/contributor?post=836"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/businesstechnicalmath\/wp-json\/wp\/v2\/license?post=836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}