{"id":1861,"date":"2021-12-02T19:39:46","date_gmt":"2021-12-03T00:39:46","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-5-7\/"},"modified":"2022-11-02T10:37:59","modified_gmt":"2022-11-02T14:37:59","slug":"answer-key-5-7","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-5-7\/","title":{"raw":"Answer Key 5.7","rendered":"Answer Key 5.7"},"content":{"raw":"
    \n \t
  1. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rr}\n\\begin{array}[t]{rrrrr}\n&&3H&=&30 \\\\\n&&H&=&10 \\\\ \\\\\nH&+&4S&=&18 \\\\\n10&+&4S&=&18 \\\\\n-10&&&&-10 \\\\\n\\hline\n&&\\dfrac{4S}{4}&=&\\dfrac{8}{4} \\\\ \\\\\n&&S&=&2\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrcrrr}\n&&2S&-&2B&=&2 \\\\\n&&2(2)&-&2B&=&2 \\\\\n&&4&-&2B&=&2 \\\\\n&&-4&&&&-4 \\\\\n\\hline\n&&&&\\dfrac{-2B}{-2}&=&\\dfrac{-2}{-2} \\\\ \\\\\n&&&&B&=&1 \\\\ \\\\\nB&+&H&\\times &S&=&? \\\\\n1&+&(10&\\times &2)&=&? \\\\\n&&1&+&20&=&21\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rr}\n\\begin{array}[t]{rrrrr}\n&&3B&=&30 \\\\\n&&B&=&10 \\\\ \\\\\nB&+&2H&=&20 \\\\\n10&+&2H&=&20 \\\\\n-10&&&&-10 \\\\\n\\hline\n&&\\dfrac{2H}{2}&=&\\dfrac{10}{2} \\\\ \\\\\n&&H&=&5\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrrrr}\n&&H&+&4M&=&9 \\\\\n&&5&+&4M&=&9 \\\\\n&&-5&&&&-5 \\\\\n\\hline\n&&&&4M&=&4 \\\\\n&&&&M&=&1 \\\\ \\\\\nH&+&M&\\times &B&=&? \\\\\n10&+&(5&\\times &1)&=&? \\\\\n&&10&+&5&=&15\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrl}\n\\text{Row 2}&-a&-&2b&-&2c&+&2d&=&-8 \\\\\n\\text{Row 3}&2a&-&b&-&c&-&d&=&\\phantom{-}5 \\\\\n\\text{Column 1}&a&-&b&+&c&+&2d&=&-1 \\\\\n\\text{Column 3}&a&-&2b&-&c&-&d&=&\\phantom{-}3 \\\\ \\\\\n&(-a&-&2b&-&2c&+&2d&=&-8)(2) \\\\\n&-2a&-&4b&-&4c&+&4d&=&-16 \\\\\n+&2a&-&b&-&c&-&d&=&\\phantom{-0}5 \\\\\n\\hline\n&&&-5b&-&5c&+&3d&=&-11 \\\\ \\\\\n&-a&-&2b&-&2c&+&2d&=&-8 \\\\\n+&a&-&b&+&c&+&2d&=&-1 \\\\\n\\hline\n&&&-3b&-&c&+&4d&=&-9 \\\\ \\\\\n&-a&-&2b&-&2c&+&2d&=&-8 \\\\\n+&a&-&2b&-&c&-&d&=&\\phantom{-}3 \\\\\n\\hline\n&&&(-4b&-&3c&+&d&=&-5)(-4) \\\\\n&&&16b&+&12c&-&4d&=&20 \\\\\n&&+&-3b&-&c&+&4d&=&-9 \\\\\n\\hline\n&&&&&13b&+&11c&=&11 \\\\ \\\\\n&&&(-4b&-&3c&+&d&=&-5)(-3) \\\\\n&&&12b&+&9c&-&3d&=&\\phantom{-}15 \\\\\n&&+&-5b&-&5c&+&3d&=&-11 \\\\\n\\hline\n&&&&&7b&+&4c&=&4\n\\end{array}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrl}\n&&&&(13b&+&11c&=&11)(-4) \\\\\n&&&&(\\phantom{0}7b&+&4c&=&\\phantom{0}4)(11) \\\\ \\\\\n&&&&-52b&-&44c&=&-44 \\\\\n&&&+&77b&+&44c&=&\\phantom{-}44 \\\\\n\\hline\n&&&&&&25b&=&0 \\\\\n&&&&&&b&=&0 \\\\ \\\\\n&&&&7b&+&4c&=&4 \\\\\n&&&&7(0)&+&4c&=&4 \\\\\n&&&&&&\\dfrac{4c}{4}&=&\\dfrac{4}{4} \\\\ \\\\\n&&&&&&c&=&1 \\\\ \\\\\n&&-4b&-&3c&+&d&=&-5 \\\\\n&&-4(0)&-&3(1)&+&d&=&-5 \\\\\n&&&&-3&+&d&=&-5 \\\\\n&&&&+3&&&&+3 \\\\\n\\hline\n&&&&&&d&=&-2 \\\\ \\\\\na&-&2b&-&c&-&d&=&\\phantom{-}3 \\\\\na&-&2(0)&-&1&-&(-2)&=&\\phantom{-}3 \\\\\n&&a&-&1&+&2&=&\\phantom{-}3 \\\\\n&&&&a&+&1&=&\\phantom{-}3 \\\\\n&&&&&-&1&&-1 \\\\\n\\hline\n&&&&&&a&=&2\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rr} \\begin{array}[t]{rrrrr} &&3H&=&30 \\\\ &&H&=&10 \\\\ \\\\ H&+&4S&=&18 \\\\ 10&+&4S&=&18 \\\\ -10&&&&-10 \\\\ \\hline &&\\dfrac{4S}{4}&=&\\dfrac{8}{4} \\\\ \\\\ &&S&=&2 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrcrrr} &&2S&-&2B&=&2 \\\\ &&2(2)&-&2B&=&2 \\\\ &&4&-&2B&=&2 \\\\ &&-4&&&&-4 \\\\ \\hline &&&&\\dfrac{-2B}{-2}&=&\\dfrac{-2}{-2} \\\\ \\\\ &&&&B&=&1 \\\\ \\\\ B&+&H&\\times &S&=&? \\\\ 1&+&(10&\\times &2)&=&? \\\\ &&1&+&20&=&21 \\end{array} \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rr} \\begin{array}[t]{rrrrr} &&3B&=&30 \\\\ &&B&=&10 \\\\ \\\\ B&+&2H&=&20 \\\\ 10&+&2H&=&20 \\\\ -10&&&&-10 \\\\ \\hline &&\\dfrac{2H}{2}&=&\\dfrac{10}{2} \\\\ \\\\ &&H&=&5 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrrrr} &&H&+&4M&=&9 \\\\ &&5&+&4M&=&9 \\\\ &&-5&&&&-5 \\\\ \\hline &&&&4M&=&4 \\\\ &&&&M&=&1 \\\\ \\\\ H&+&M&\\times &B&=&? \\\\ 10&+&(5&\\times &1)&=&? \\\\ &&10&+&5&=&15 \\end{array} \\end{array}[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrl} \\text{Row 2}&-a&-&2b&-&2c&+&2d&=&-8 \\\\ \\text{Row 3}&2a&-&b&-&c&-&d&=&\\phantom{-}5 \\\\ \\text{Column 1}&a&-&b&+&c&+&2d&=&-1 \\\\ \\text{Column 3}&a&-&2b&-&c&-&d&=&\\phantom{-}3 \\\\ \\\\ &(-a&-&2b&-&2c&+&2d&=&-8)(2) \\\\ &-2a&-&4b&-&4c&+&4d&=&-16 \\\\ +&2a&-&b&-&c&-&d&=&\\phantom{-0}5 \\\\ \\hline &&&-5b&-&5c&+&3d&=&-11 \\\\ \\\\ &-a&-&2b&-&2c&+&2d&=&-8 \\\\ +&a&-&b&+&c&+&2d&=&-1 \\\\ \\hline &&&-3b&-&c&+&4d&=&-9 \\\\ \\\\ &-a&-&2b&-&2c&+&2d&=&-8 \\\\ +&a&-&2b&-&c&-&d&=&\\phantom{-}3 \\\\ \\hline &&&(-4b&-&3c&+&d&=&-5)(-4) \\\\ &&&16b&+&12c&-&4d&=&20 \\\\ &&+&-3b&-&c&+&4d&=&-9 \\\\ \\hline &&&&&13b&+&11c&=&11 \\\\ \\\\ &&&(-4b&-&3c&+&d&=&-5)(-3) \\\\ &&&12b&+&9c&-&3d&=&\\phantom{-}15 \\\\ &&+&-5b&-&5c&+&3d&=&-11 \\\\ \\hline &&&&&7b&+&4c&=&4 \\end{array}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrl} &&&&(13b&+&11c&=&11)(-4) \\\\ &&&&(\\phantom{0}7b&+&4c&=&\\phantom{0}4)(11) \\\\ \\\\ &&&&-52b&-&44c&=&-44 \\\\ &&&+&77b&+&44c&=&\\phantom{-}44 \\\\ \\hline &&&&&&25b&=&0 \\\\ &&&&&&b&=&0 \\\\ \\\\ &&&&7b&+&4c&=&4 \\\\ &&&&7(0)&+&4c&=&4 \\\\ &&&&&&\\dfrac{4c}{4}&=&\\dfrac{4}{4} \\\\ \\\\ &&&&&&c&=&1 \\\\ \\\\ &&-4b&-&3c&+&d&=&-5 \\\\ &&-4(0)&-&3(1)&+&d&=&-5 \\\\ &&&&-3&+&d&=&-5 \\\\ &&&&+3&&&&+3 \\\\ \\hline &&&&&&d&=&-2 \\\\ \\\\ a&-&2b&-&c&-&d&=&\\phantom{-}3 \\\\ a&-&2(0)&-&1&-&(-2)&=&\\phantom{-}3 \\\\ &&a&-&1&+&2&=&\\phantom{-}3 \\\\ &&&&a&+&1&=&\\phantom{-}3 \\\\ &&&&&-&1&&-1 \\\\ \\hline &&&&&&a&=&2 \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":48,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1861","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1861","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1861\/revisions"}],"predecessor-version":[{"id":1862,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1861\/revisions\/1862"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1861\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1861"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1861"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1861"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1861"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}