{"id":1851,"date":"2021-12-02T19:39:42","date_gmt":"2021-12-03T00:39:42","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-5-2\/"},"modified":"2022-11-02T10:37:53","modified_gmt":"2022-11-02T14:37:53","slug":"answer-key-5-2","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-5-2\/","title":{"raw":"Answer Key 5.2","rendered":"Answer Key 5.2"},"content":{"raw":"
    \n \t
  1. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n-3x&=&6x&-&9 \\\\\n-6x&&-6x&& \\\\\n\\hline\n\\dfrac{-9x}{-9}&=&\\dfrac{-9}{-9}&& \\\\ \\\\\nx&=&1&& \\\\ \\\\\n\\therefore y&=&-3(1)&& \\\\\ny&=&-3&& \\\\ \\\\\n(1,-3)&&&&\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\nx&+&5&=&-2x&-&4 \\\\\n+2x&-&5&&+2x&-&5 \\\\\n\\hline\n&&\\dfrac{3x}{3}&=&\\dfrac{-9}{3}&& \\\\ \\\\\n&&x&=&-3&& \\\\ \\\\\n&&\\therefore y&=&-3&+&5 \\\\\n&&y&=&2&& \\\\ \\\\\n(-3,2)&&&&&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n2x&-&1&=&-2x&-&9 \\\\\n+2x&+&1&&+2x&+&1 \\\\\n\\hline\n&&\\dfrac{4x}{4}&=&\\dfrac{-8}{4}&& \\\\ \\\\\n&&x&=&-2&& \\\\ \\\\\n&&\\therefore y&=&2(-2)&-&1 \\\\\n&&y&=&-4&-&1 \\\\\n&&y&=&-5&& \\\\\n(-2,-5)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n6x&+&3&=&-6x&+&3 \\\\\n+6x&-&3&&+6x&-&3 \\\\\n\\hline\n&&\\dfrac{12x}{12}&=&\\dfrac{0}{12}&& \\\\ \\\\\n&&x&=&0&& \\\\ \\\\\n&&\\therefore y&=&6(0)&+&3 \\\\\n&&y&=&3&& \\\\\n(0,3)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n6x&+&4&=&-3x&-&5 \\\\\n+3x&-&4&&+3x&-&4 \\\\\n\\hline\n&&\\dfrac{9x}{9}&=&\\dfrac{-9}{9}&& \\\\ \\\\\n&&x&=&-1&& \\\\ \\\\\n&&\\therefore y&=&6(-1)&+&4 \\\\\n&&y&=&-6&+&4 \\\\\n&&y&=&-2&& \\\\\n(-1,-2)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n3x&+&13&=&-2x&-&22 \\\\\n+2x&-&13&&+2x&-&13 \\\\\n\\hline\n&&\\dfrac{5x}{5}&=&\\dfrac{-35}{5}&& \\\\ \\\\\n&&x&=&-7&& \\\\ \\\\\n&&\\therefore y&=&3(-7)&+&13 \\\\\n&&y&=&-21&+&13 \\\\\n&&y&=&-8&& \\\\\n(-7,-8)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n3x&+&2&=&-3x&+&8 \\\\\n+3x&-&2&&+3x&-&2 \\\\\n\\hline\n&&\\dfrac{6x}{6}&=&\\dfrac{6}{6}&& \\\\ \\\\\n&&x&=&1&& \\\\ \\\\\n&&\\therefore y&=&3(1)&+&2 \\\\\n&&y&=&3&+&2 \\\\\n&&y&=&5&& \\\\\n(1,5)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n-2x&-&9&=&-5x&-&21 \\\\\n+5x&+&9&&+5x&+&9 \\\\\n\\hline\n&&\\dfrac{3x}{3}&=&\\dfrac{-12}{3}&& \\\\ \\\\\n&&x&=&-4&& \\\\ \\\\\n&&\\therefore y&=&-2(-4)&-&9 \\\\\n&&y&=&8&-&9 \\\\\n&&y&=&-1&& \\\\\n(-4,-1)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n2x&-&3&=&-2x&+&9 \\\\\n+2x&+&3&&+2x&+&3 \\\\\n\\hline\n&&\\dfrac{4x}{4}&=&\\dfrac{12}{4}&& \\\\ \\\\\n&&x&=&3&& \\\\ \\\\\n&&\\therefore y&=&2(3)&-&3 \\\\\n&&y&=&6&-&3 \\\\\n&&y&=&3&& \\\\\n(3,3)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n7x&-&24&=&-3x&+&16 \\\\\n+3x&+&24&&+3x&+&24 \\\\\n\\hline\n&&\\dfrac{10x}{10}&=&\\dfrac{40}{10}&& \\\\ \\\\\n&&x&=&4&& \\\\ \\\\\n&&\\therefore y&=&7(4)&-&24 \\\\\n&&y&=&28&-&24 \\\\\n&&y&=&4&& \\\\\n(4,4)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n3x&-&3(3x&-&4)&=&-6 \\\\\n3x&-&9x&+&12&=&-6 \\\\\n&&&-&12&&-12 \\\\\n\\hline\n&&&&\\dfrac{-6x}{-6}&=&\\dfrac{-18}{-6} \\\\ \\\\\n&&&&x&=&3 \\\\ \\\\\n&&&&\\therefore y&=&3(3)-4 \\\\\n&&&&y&=&9-4 \\\\\n&&&&y&=&5 \\\\\n(3,5)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n-x&+&3(6x&+&21)&=&\\phantom{-}12 \\\\\n-x&+&18x&+&63&=&\\phantom{-}12 \\\\\n&&&-&63&&-63 \\\\\n\\hline\n&&&&\\dfrac{17x}{17}&=&\\dfrac{-51}{17} \\\\ \\\\\n&&&&x&=&-3 \\\\ \\\\\n&&&&\\therefore y&=&6(-3)+21 \\\\\n&&&&y&=&-18+21 \\\\\n&&&&y&=&3 \\\\\n(-3,3)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n3x&-&6(-6)&=&30 \\\\\n3x&+&36&=&30 \\\\\n&-&36&&-36 \\\\\n\\hline\n&&\\dfrac{3x}{3}&=&\\dfrac{-6}{3} \\\\ \\\\\n&&x&=&-2 \\\\ \\\\\n&&y&=&-6 \\\\\n(-2,-6)&&&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n6x&-&4(-6x&+&2)&=&-8 \\\\\n6x&+&24x&-&8&=&-8 \\\\\n&&&+&8&&+8 \\\\\n\\hline\n&&&&\\dfrac{30x}{30}&=&\\dfrac{0}{30} \\\\ \\\\\n&&&&\\therefore x&=&0 \\\\ \\\\\n&&&&\\therefore y&=&-6(0)+2 \\\\\n&&&&y&=&0+2 \\\\\n&&&&y&=&2 \\\\\n(0,2)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrr}\n3x&+&4(-5)&=&-17 \\\\\n3x&-&20&=&-17 \\\\\n&+&20&&+20 \\\\\n\\hline\n&&\\dfrac{3x}{3}&=&\\dfrac{3}{3} \\\\ \\\\\n&&x&=&1 \\\\ \\\\\n&&y&=&-5 \\\\\n(1,-5)&&&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n7x&+&2(5x&+&5)&=&-7 \\\\\n7x&+&10x&+&10&=&-7 \\\\\n&&&-&10&&-10 \\\\\n\\hline\n&&&&\\dfrac{17x}{17}&=&\\dfrac{-17}{17} \\\\ \\\\\n&&&&x&=&-1 \\\\ \\\\\n&&&&\\therefore y&=&5(-1)+5 \\\\\n&&&&y&=&-5+5 \\\\\n&&&&y&=&0 \\\\\n(-1,0)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  17. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n-6x&+&6y&=&-12&(\\div &6) \\\\\n-x&+&y&=&-2&& \\\\\n+x&&&&+x&& \\\\\n\\hline\n&&y&=&x&-&2 \\\\ \\\\\n8x&-&3(x&-&2)&=&16 \\\\\n8x&-&3x&+&6&=&16 \\\\\n&&&-&6&&-6 \\\\\n\\hline\n&&&&\\dfrac{5x}{5}&=&\\dfrac{10}{5} \\\\ \\\\\n&&&&x&=&2 \\\\ \\\\\n&&&&\\therefore y&=&x-2 \\\\\n&&&&y&=&2-2=0 \\\\\n(2,0)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  18. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n-8x&+&2y&=&-6&(\\div &2) \\\\\n-4x&+&y&=&-3&& \\\\\n+4x&&&&+4x&& \\\\\n\\hline\n&&y&=&4x&-&3 \\\\ \\\\\n-2x&+&3(4x&-&3)&=&11 \\\\\n-2x&+&12x&-&9&=&11 \\\\\n&&&+&9&&+9 \\\\\n\\hline\n&&&&\\dfrac{10x}{10}&=&\\dfrac{20}{10} \\\\ \\\\\n&&&&x&=&2 \\\\ \\\\\n&&&&\\therefore y&=&4(2)-3 \\\\\n&&&&y&=&8-3=5 \\\\\n(2,5)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  19. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n-7x&-&y&=&20&& \\\\\n-20&+&y&&-20&+&y \\\\\n\\hline\n-7x&-&20&=&y&& \\\\ \\\\\n2x&+&3(-7x&-&20)&=&\\phantom{+}16 \\\\\n2x&-&21x&-&60&=&\\phantom{+}16 \\\\\n&&&+&60&&+60 \\\\\n\\hline\n&&&&\\dfrac{-19x}{-19}&=&\\dfrac{76}{-19} \\\\ \\\\\n&&&&x&=&-4 \\\\ \\\\\n&&&&\\therefore y&=&-7(-4)-20 \\\\\n&&&&y&=&28-20 \\\\\n&&&&y&=&8 \\\\\n(-4,8)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  20. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrll}\n&&(-x&-&4y&=&-14)&(-1)& \\\\\n&&x&+&4y&=&14&& \\\\\n&&&-&4y&&-4y&& \\\\\n\\hline\n&&&&x&=&14&-&4y \\\\ \\\\\n&&(-6x&+&8y&=&12)&\\div &2 \\\\\n&&-3x&+&4y&=&6&& \\\\\n-3(14&-&4y)&+&4y&=&6&& \\\\\n-42&+&12y&+&4y&=&6&& \\\\\n+42&&&&&&+42&& \\\\\n\\hline\n&&&&\\dfrac{16y}{16}&=&\\dfrac{48}{16}&& \\\\ \\\\\n&&&&y&=&3&& \\\\ \\\\\n&&&&x&=&14&-&4(3) \\\\\n&&&&x&=&14&-&12 \\\\\n&&&&x&=&2&& \\\\\n(2,3)&&&&&&&&\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} -3x&=&6x&-&9 \\\\ -6x&&-6x&& \\\\ \\hline \\dfrac{-9x}{-9}&=&\\dfrac{-9}{-9}&& \\\\ \\\\ x&=&1&& \\\\ \\\\ \\therefore y&=&-3(1)&& \\\\ y&=&-3&& \\\\ \\\\ (1,-3)&&&& \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} x&+&5&=&-2x&-&4 \\\\ +2x&-&5&&+2x&-&5 \\\\ \\hline &&\\dfrac{3x}{3}&=&\\dfrac{-9}{3}&& \\\\ \\\\ &&x&=&-3&& \\\\ \\\\ &&\\therefore y&=&-3&+&5 \\\\ &&y&=&2&& \\\\ \\\\ (-3,2)&&&&&& \\\\ \\end{array}[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 2x&-&1&=&-2x&-&9 \\\\ +2x&+&1&&+2x&+&1 \\\\ \\hline &&\\dfrac{4x}{4}&=&\\dfrac{-8}{4}&& \\\\ \\\\ &&x&=&-2&& \\\\ \\\\ &&\\therefore y&=&2(-2)&-&1 \\\\ &&y&=&-4&-&1 \\\\ &&y&=&-5&& \\\\ (-2,-5)&&&&&& \\end{array}[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 6x&+&3&=&-6x&+&3 \\\\ +6x&-&3&&+6x&-&3 \\\\ \\hline &&\\dfrac{12x}{12}&=&\\dfrac{0}{12}&& \\\\ \\\\ &&x&=&0&& \\\\ \\\\ &&\\therefore y&=&6(0)&+&3 \\\\ &&y&=&3&& \\\\ (0,3)&&&&&& \\end{array}[\/latex]<\/li>\n
    5. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 6x&+&4&=&-3x&-&5 \\\\ +3x&-&4&&+3x&-&4 \\\\ \\hline &&\\dfrac{9x}{9}&=&\\dfrac{-9}{9}&& \\\\ \\\\ &&x&=&-1&& \\\\ \\\\ &&\\therefore y&=&6(-1)&+&4 \\\\ &&y&=&-6&+&4 \\\\ &&y&=&-2&& \\\\ (-1,-2)&&&&&& \\end{array}[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 3x&+&13&=&-2x&-&22 \\\\ +2x&-&13&&+2x&-&13 \\\\ \\hline &&\\dfrac{5x}{5}&=&\\dfrac{-35}{5}&& \\\\ \\\\ &&x&=&-7&& \\\\ \\\\ &&\\therefore y&=&3(-7)&+&13 \\\\ &&y&=&-21&+&13 \\\\ &&y&=&-8&& \\\\ (-7,-8)&&&&&& \\end{array}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 3x&+&2&=&-3x&+&8 \\\\ +3x&-&2&&+3x&-&2 \\\\ \\hline &&\\dfrac{6x}{6}&=&\\dfrac{6}{6}&& \\\\ \\\\ &&x&=&1&& \\\\ \\\\ &&\\therefore y&=&3(1)&+&2 \\\\ &&y&=&3&+&2 \\\\ &&y&=&5&& \\\\ (1,5)&&&&&& \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} -2x&-&9&=&-5x&-&21 \\\\ +5x&+&9&&+5x&+&9 \\\\ \\hline &&\\dfrac{3x}{3}&=&\\dfrac{-12}{3}&& \\\\ \\\\ &&x&=&-4&& \\\\ \\\\ &&\\therefore y&=&-2(-4)&-&9 \\\\ &&y&=&8&-&9 \\\\ &&y&=&-1&& \\\\ (-4,-1)&&&&&& \\end{array}[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 2x&-&3&=&-2x&+&9 \\\\ +2x&+&3&&+2x&+&3 \\\\ \\hline &&\\dfrac{4x}{4}&=&\\dfrac{12}{4}&& \\\\ \\\\ &&x&=&3&& \\\\ \\\\ &&\\therefore y&=&2(3)&-&3 \\\\ &&y&=&6&-&3 \\\\ &&y&=&3&& \\\\ (3,3)&&&&&& \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 7x&-&24&=&-3x&+&16 \\\\ +3x&+&24&&+3x&+&24 \\\\ \\hline &&\\dfrac{10x}{10}&=&\\dfrac{40}{10}&& \\\\ \\\\ &&x&=&4&& \\\\ \\\\ &&\\therefore y&=&7(4)&-&24 \\\\ &&y&=&28&-&24 \\\\ &&y&=&4&& \\\\ (4,4)&&&&&& \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} 3x&-&3(3x&-&4)&=&-6 \\\\ 3x&-&9x&+&12&=&-6 \\\\ &&&-&12&&-12 \\\\ \\hline &&&&\\dfrac{-6x}{-6}&=&\\dfrac{-18}{-6} \\\\ \\\\ &&&&x&=&3 \\\\ \\\\ &&&&\\therefore y&=&3(3)-4 \\\\ &&&&y&=&9-4 \\\\ &&&&y&=&5 \\\\ (3,5)&&&&&& \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} -x&+&3(6x&+&21)&=&\\phantom{-}12 \\\\ -x&+&18x&+&63&=&\\phantom{-}12 \\\\ &&&-&63&&-63 \\\\ \\hline &&&&\\dfrac{17x}{17}&=&\\dfrac{-51}{17} \\\\ \\\\ &&&&x&=&-3 \\\\ \\\\ &&&&\\therefore y&=&6(-3)+21 \\\\ &&&&y&=&-18+21 \\\\ &&&&y&=&3 \\\\ (-3,3)&&&&&& \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 3x&-&6(-6)&=&30 \\\\ 3x&+&36&=&30 \\\\ &-&36&&-36 \\\\ \\hline &&\\dfrac{3x}{3}&=&\\dfrac{-6}{3} \\\\ \\\\ &&x&=&-2 \\\\ \\\\ &&y&=&-6 \\\\ (-2,-6)&&&& \\\\ \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} 6x&-&4(-6x&+&2)&=&-8 \\\\ 6x&+&24x&-&8&=&-8 \\\\ &&&+&8&&+8 \\\\ \\hline &&&&\\dfrac{30x}{30}&=&\\dfrac{0}{30} \\\\ \\\\ &&&&\\therefore x&=&0 \\\\ \\\\ &&&&\\therefore y&=&-6(0)+2 \\\\ &&&&y&=&0+2 \\\\ &&&&y&=&2 \\\\ (0,2)&&&&&& \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrr} 3x&+&4(-5)&=&-17 \\\\ 3x&-&20&=&-17 \\\\ &+&20&&+20 \\\\ \\hline &&\\dfrac{3x}{3}&=&\\dfrac{3}{3} \\\\ \\\\ &&x&=&1 \\\\ \\\\ &&y&=&-5 \\\\ (1,-5)&&&& \\\\ \\end{array}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} 7x&+&2(5x&+&5)&=&-7 \\\\ 7x&+&10x&+&10&=&-7 \\\\ &&&-&10&&-10 \\\\ \\hline &&&&\\dfrac{17x}{17}&=&\\dfrac{-17}{17} \\\\ \\\\ &&&&x&=&-1 \\\\ \\\\ &&&&\\therefore y&=&5(-1)+5 \\\\ &&&&y&=&-5+5 \\\\ &&&&y&=&0 \\\\ (-1,0)&&&&&& \\end{array}[\/latex]<\/li>\n
    17. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} -6x&+&6y&=&-12&(\\div &6) \\\\ -x&+&y&=&-2&& \\\\ +x&&&&+x&& \\\\ \\hline &&y&=&x&-&2 \\\\ \\\\ 8x&-&3(x&-&2)&=&16 \\\\ 8x&-&3x&+&6&=&16 \\\\ &&&-&6&&-6 \\\\ \\hline &&&&\\dfrac{5x}{5}&=&\\dfrac{10}{5} \\\\ \\\\ &&&&x&=&2 \\\\ \\\\ &&&&\\therefore y&=&x-2 \\\\ &&&&y&=&2-2=0 \\\\ (2,0)&&&&&& \\end{array}[\/latex]<\/li>\n
    18. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} -8x&+&2y&=&-6&(\\div &2) \\\\ -4x&+&y&=&-3&& \\\\ +4x&&&&+4x&& \\\\ \\hline &&y&=&4x&-&3 \\\\ \\\\ -2x&+&3(4x&-&3)&=&11 \\\\ -2x&+&12x&-&9&=&11 \\\\ &&&+&9&&+9 \\\\ \\hline &&&&\\dfrac{10x}{10}&=&\\dfrac{20}{10} \\\\ \\\\ &&&&x&=&2 \\\\ \\\\ &&&&\\therefore y&=&4(2)-3 \\\\ &&&&y&=&8-3=5 \\\\ (2,5)&&&&&& \\end{array}[\/latex]<\/li>\n
    19. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} -7x&-&y&=&20&& \\\\ -20&+&y&&-20&+&y \\\\ \\hline -7x&-&20&=&y&& \\\\ \\\\ 2x&+&3(-7x&-&20)&=&\\phantom{+}16 \\\\ 2x&-&21x&-&60&=&\\phantom{+}16 \\\\ &&&+&60&&+60 \\\\ \\hline &&&&\\dfrac{-19x}{-19}&=&\\dfrac{76}{-19} \\\\ \\\\ &&&&x&=&-4 \\\\ \\\\ &&&&\\therefore y&=&-7(-4)-20 \\\\ &&&&y&=&28-20 \\\\ &&&&y&=&8 \\\\ (-4,8)&&&&&& \\end{array}[\/latex]<\/li>\n
    20. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrll} &&(-x&-&4y&=&-14)&(-1)& \\\\ &&x&+&4y&=&14&& \\\\ &&&-&4y&&-4y&& \\\\ \\hline &&&&x&=&14&-&4y \\\\ \\\\ &&(-6x&+&8y&=&12)&\\div &2 \\\\ &&-3x&+&4y&=&6&& \\\\ -3(14&-&4y)&+&4y&=&6&& \\\\ -42&+&12y&+&4y&=&6&& \\\\ +42&&&&&&+42&& \\\\ \\hline &&&&\\dfrac{16y}{16}&=&\\dfrac{48}{16}&& \\\\ \\\\ &&&&y&=&3&& \\\\ \\\\ &&&&x&=&14&-&4(3) \\\\ &&&&x&=&14&-&12 \\\\ &&&&x&=&2&& \\\\ (2,3)&&&&&&&& \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":43,"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-1851","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\/1851","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\/1851\/revisions"}],"predecessor-version":[{"id":1852,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1851\/revisions\/1852"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1851\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1851"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1851"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1851"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}