{"id":1853,"date":"2021-12-02T19:39:43","date_gmt":"2021-12-03T00:39:43","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-5-3\/"},"modified":"2022-11-02T10:37:54","modified_gmt":"2022-11-02T14:37:54","slug":"answer-key-5-3","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-5-3\/","title":{"raw":"Answer Key 5.3","rendered":"Answer Key 5.3"},"content":{"raw":"
    \n \t
  1. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n&4x&+&2y&=&0 \\\\\n+&-4x&-&9y&=&-28 \\\\\n\\hline\n&&&\\dfrac{-7y}{-7}&=&\\dfrac{-28}{-7} \\\\ \\\\\n&&&y&=&4 \\\\ \\\\\n&4x&+&2(4)&=&0 \\\\\n&4x&+&8&=&0 \\\\\n&&-&8&&-8 \\\\\n\\hline\n&&&\\dfrac{4x}{4}&=&\\dfrac{-8}{4} \\\\ \\\\\n&&&x&=&-2 \\\\\n(-2,4)&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrr}\n&-7x&+&y&=&-10 \\\\\n+&-9x&-&y&=&-22 \\\\\n\\hline\n&&&\\dfrac{-16x}{-16}&=&\\dfrac{-32}{-16} \\\\ \\\\\n&&&x&=&2 \\\\ \\\\\n&-7(2)&+&y&=&-10 \\\\\n&-14&+&y&=&-10 \\\\\n&+14&&&&+14 \\\\\n\\hline\n&&&y&=&4 \\\\\n(2,4)&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n&-9x&+&5y&=&-22 \\\\\n+&9x&-&5y&=&13 \\\\\n\\hline\n&&&0&=&-9\n\\end{array}\\\\ \\therefore \\text{Two parallel lines. No solution}[\/latex]<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n&-x&-&2y&=&-7 \\\\\n+&x&+&2y&=&7 \\\\\n\\hline\n&&&0&=&0\\\\\n\\end{array}\\\\ \\therefore \\text{Two identical lines. Infinite solutions}[\/latex]<\/li>\n \t
  5. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n&-6x&+&9y&=&3 \\\\\n+&6x&-&9y&=&-9 \\\\\n\\hline\n&&&0&=&-6\n\\end{array}\\\\ \\therefore \\text{Two parallel lines. No solution}[\/latex]<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&5x&-&5y&=&-15&(\\div 5) \\\\\n&(x&-&y&=&-3)&(-1) \\\\ \\\\\n&x&-&y&=&-3& \\\\\n+&-x&+&y&=&3& \\\\\n\\hline\n&&&0&=&0& \\\\\n\\end{array}\\\\ \\therefore \\text{Two identical lines. Infinite solutions}[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n&4x&-&6y&=&-10 \\\\\n+&4x&+&6y&=&-14 \\\\\n\\hline\n&&&\\dfrac{8x}{8}&=&\\dfrac{-24}{8} \\\\ \\\\\n&&&x&=&-3 \\\\ \\\\\n&4(-3)&-&6y&=&-10 \\\\\n&-12&-&6y&=&-10 \\\\\n&+12&&&&+12 \\\\\n\\hline\n&&&\\dfrac{-6y}{-6}&=&\\dfrac{2}{-6} \\\\ \\\\\n&&&y&=&-\\dfrac{1}{3} \\\\\n(-3, -\\dfrac{1}{3})&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrl}\n&-3x&+&3y&=&-12&\\div &(-3) \\\\\n&-3x&+&9y&=&-24&\\div &(3) \\\\ \\\\\n& x&-&y&=&4&& \\\\\n+&-x&+&3y&=&-8&& \\\\\n\\hline\n&&&\\dfrac{2y}{2}&=&\\dfrac{-4}{2}&& \\\\ \\\\\n&&&y&=&-2&& \\\\ \\\\\n&\\therefore x&-&y&=&4&& \\\\\n&x&-&-2&=&4&& \\\\\n&x&+&2&=&4&& \\\\\n&&-&2&&-2&& \\\\\n\\hline\n&&&x&=&2&& \\\\\n(2,-2)&&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&(-x&-&5y&=&28)&(-1) \\\\ \\\\\n&x&+&5y&=&-28& \\\\\n+&-x&+&4y&=&-17& \\\\\n\\hline\n&&&\\dfrac{9y}{9}&=&\\dfrac{-45}{9}& \\\\ \\\\\n&&&y&=&-5& \\\\ \\\\\n&x&+&5(-5)&=&-28& \\\\\n&x&-&25&=&-28& \\\\\n&&+&25&&+25& \\\\\n\\hline\n&&&x&=&-3& \\\\\n(-3,-5)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&(-10x&-&5y&=&0)&(-1) \\\\ \\\\\n&10x&+&5y&=&0& \\\\\n+&-10x&-&10y&=&-30& \\\\\n\\hline\n&&&\\dfrac{-5y}{-5}&=&\\dfrac{-30}{-5}& \\\\ \\\\\n&&&y&=&6& \\\\ \\\\\n&10x&+&5(6)&=&0& \\\\\n&10x&+&30&=&0& \\\\\n&&-&30&&-30& \\\\\n\\hline\n&&&\\dfrac{10x}{10}&=&\\dfrac{-30}{10}& \\\\ \\\\\n&&&x&=&-3& \\\\\n(-3,6)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&(2x&-&y&=&5)&(2) \\\\ \\\\\n&4x&-&2y&=&10& \\\\\n+&5x&+&2y&=&-28& \\\\\n\\hline\n&&&\\dfrac{9x}{9}&=&\\dfrac{-18}{9}& \\\\ \\\\\n&&&x&=&-2& \\\\ \\\\\n&2(x)&-&y&=&5& \\\\\n&2(-2)&-&y&=&5& \\\\\n&-4&-&y&=&5& \\\\\n&+4&&&&+4& \\\\\n\\hline\n&&&-y&=&9& \\\\ \\\\\n&&&y&=&-9& \\\\\n(-2,-9)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&-5x&+&6y&=&-17& \\\\\n&(x&-&2y&=&5)&(3) \\\\ \\\\\n&-5x&+&6y&=&-17& \\\\\n+&3x&-&6y&=&15& \\\\\n\\hline\n&&&\\dfrac{-2x}{-2}&=&\\dfrac{-2}{-2}& \\\\ \\\\\n&&&x&=&1& \\\\ \\\\\n&x&-&2y&=&5& \\\\\n&1&-&2y&=&5& \\\\\n&-1&&&&-1& \\\\\n\\hline\n&&&\\dfrac{-2y}{-2}&=&\\dfrac{4}{-2}& \\\\ \\\\\n&&&y&=&-2& \\\\\n(1,-2)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&(10x&+&6y&=&24)&(\\div 2) \\\\\n&(-6x&+&y&=&4)&(-3) \\\\ \\\\\n&5x&+&3y&=&12& \\\\\n+&18x&-&3y&=&-12& \\\\\n\\hline\n&&&23x&=&0& \\\\\n&&&x&=&0& \\\\ \\\\\n&-6(x)&+&y&=&4& \\\\\n&-6(0)&+&y&=&4& \\\\\n&&&y&=&4& \\\\\n(0,4)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&(10x&+&6y&=&-10)&(\\div -2) \\\\ \\\\\n&x&+&3y&=&-1& \\\\\n+&-5x&-&3y&=&5& \\\\\n\\hline\n&&&\\dfrac{-4x}{-4}&=&\\dfrac{4}{-4}& \\\\ \\\\\n&&&x&=&-1& \\\\ \\\\\n&-1&+&3y&=&-1& \\\\\n&+1&&&&+1& \\\\\n\\hline\n&&&3y&=&0& \\\\ \\\\\n&&&y&=&0& \\\\\n(-1,0)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n&(2x&+&4y&=&24)&(\\div 2) \\\\\n&(4x&-&12y&=&8)&(\\div -4) \\\\ \\\\\n&x&+&2y&=&12& \\\\\n+&-x&+&3y&=&-2& \\\\\n\\hline\n&&&\\dfrac{5y}{5}&=&\\dfrac{10}{5}& \\\\ \\\\\n&&&y&=&2& \\\\ \\\\\n&x&+&2(y)&=&12& \\\\\n&x&+&2(2)&=&12& \\\\\n&x&+&4&=&12& \\\\\n&&-&4&&-4& \\\\\n\\hline\n&&&x&=&8& \\\\\n(8,2)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n&(-6x&+&4y&=&12)&(\\div 2) \\\\\n&(12x&+&6y&=&18)&(\\div -3) \\\\ \\\\\n&-3x&+&2y&=&6& \\\\\n+&-4x&-&2y&=&-6& \\\\\n\\hline\n&&&-7x&=&0& \\\\\n&&&x&=&0& \\\\ \\\\\n&\\dfrac{-3(x)}{2}&+&\\dfrac{2y}{2}&=&\\dfrac{6}{2}& \\\\ \\\\\n&\\dfrac{-3(0)}{2}&+&\\dfrac{2y}{2}&=&\\dfrac{6}{2}& \\\\ \\\\\n&&&y&=&3& \\\\\n(0,3)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  17. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&(10x&-&8y&=&-8)&(\\div 2) \\\\ \\\\\n&-7x&+&4y&=&-4& \\\\\n+&5x&-&4y&=&-4& \\\\\n\\hline\n&&&\\dfrac{-2x}{-2}&=&\\dfrac{-8}{-2}& \\\\ \\\\\n&&&x&=&4& \\\\ \\\\\n&5(4)&-&4y&=&-4& \\\\\n&20&-&4y&=&-4& \\\\\n&-20&&&&-20& \\\\\n\\hline\n&&&\\dfrac{-4y}{-4}&=&\\dfrac{-24}{-4}& \\\\ \\\\\n&&&y&=&6& \\\\\n(4,6)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  18. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&(-6x&+&4y&=&4)&(\\div 2) \\\\ \\\\\n&-3x&+&2y&=&2& \\\\\n+&3x&-&y&=&26& \\\\\n\\hline\n&&&y&=&28& \\\\ \\\\\n&3x&-&28&=&26& \\\\\n&&+&28&&+28& \\\\\n\\hline\n&&&\\dfrac{3x}{3}&=&\\dfrac{54}{3}& \\\\ \\\\\n&&&x&=&18& \\\\\n(18,28)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  19. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&(-6x&-&5y&=&-3)&(2) \\\\ \\\\\n&5x&+&10y&=&20& \\\\\n+&-12x&-&10y&=&-6& \\\\\n\\hline\n&&&\\dfrac{-7x}{-7}&=&\\dfrac{14}{-7}& \\\\ \\\\\n&&&x&=&-2& \\\\ \\\\\n&5(-2)&+&10y&=&20& \\\\\n&-10&+&10y&=&20& \\\\\n&+10&&&&+10& \\\\\n\\hline\n&&&\\dfrac{10y}{10}&=&\\dfrac{30}{10}& \\\\ \\\\\n&&&y&=&3& \\\\\n(-2,3)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  20. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n&(3x&-&7y&=&-11)&(3) \\\\ \\\\\n&-9x&-&5y&=&-19& \\\\\n+&9x&-&21y&=&-33& \\\\\n\\hline\n&&&\\dfrac{-26y}{-26}&=&\\dfrac{-52}{-26}& \\\\ \\\\\n&&&y&=&2& \\\\ \\\\\n&3x&-&7(2)&=&-11& \\\\\n&3x&-&14&=&-11& \\\\\n&&+&14&&+14& \\\\\n\\hline\n&&&\\dfrac{3x}{3}&=&\\dfrac{3}{3}& \\\\ \\\\\n&&&x&=&1& \\\\\n(1,2)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  21. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n&(-7x&+&5y&=&-8)&(3) \\\\\n&(-3x&-&3y&=&12)&(5) \\\\ \\\\\n&-21x&+&15y&=&-24& \\\\\n+&-15x&-&15y&=&60& \\\\\n\\hline\n&&&\\dfrac{-36x}{-36}&=&\\dfrac{36}{-36}& \\\\ \\\\\n&&&x&=&-1& \\\\ \\\\\n&-3(-1)&-&3y&=&12& \\\\\n&3&-&3y&=&12& \\\\\n&-3&&&&-3& \\\\\n\\hline\n&&&\\dfrac{-3y}{-3}&=&\\dfrac{9}{-3}& \\\\ \\\\\n&&&y&=&-3& \\\\\n(-1,-3)&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  22. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrcll}\n&&(6x&+&3y&=&-18)&\\div &-3 \\\\ \\\\\n&&-2x&-&y&=&6&& \\\\\n&&+2x&&&&+2x&& \\\\\n\\hline\n&&&&-y&=&2x&+&6 \\\\\n&&&&y&=&-2x&-&6 \\\\ \\\\\n8x&+&7(-2x&-&6)&=&-24&& \\\\\n8x&-&14x&-&42&=&-24&& \\\\\n&&&+&42&&+42&& \\\\\n\\hline\n&&&&\\dfrac{-6x}{-6}&=&\\dfrac{18}{-6}&& \\\\ \\\\\n&&&&x&=&-3&& \\\\ \\\\\n&&&&y&=&-2(-3)&-&6 \\\\\n&&&&y&=&6&-&6 \\\\\n&&&&y&=&0&& \\\\\n(-3,0)&&&&&&&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  23. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&&(-8x&-&8y&=&-8)&\\div &(-8) \\\\ \\\\\n&&x&+&y&=&1&& \\\\\n&&-x&&&&-x&& \\\\\n\\hline\n&&&&y&=&1&-&x \\\\ \\\\\n10x&+&9(1&-&x)&=&1&& \\\\\n10x&+&9&-&9x&=&1&& \\\\\n&-&9&&&&-9&& \\\\\n\\hline\n&&&&x&=&-8&& \\\\ \\\\\n&&&&y&=&1&-&-8 \\\\\n&&&&y&=&9&& \\\\\n(-8,9)&&&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  24. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n&(-7x&+&10y&=&13)&(4) \\\\\n&(4x&+&9y&=&22)&(7) \\\\ \\\\\n&-28x&+&40y&=&52& \\\\\n+&28x&+&63y&=&154& \\\\\n\\hline\n&&&\\dfrac{103y}{103}&=&\\dfrac{206}{103}& \\\\ \\\\\n&&&y&=&2& \\\\ \\\\\n&4x&+&9(2)&=&22& \\\\\n&4x&+&18&=&22& \\\\\n&&-&18&&-18& \\\\\n\\hline\n&&&\\dfrac{4x}{4}&=&\\dfrac{4}{4}& \\\\ \\\\\n&&&x&=&1& \\\\\n(1,2)&&&&&&\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &4x&+&2y&=&0 \\\\ +&-4x&-&9y&=&-28 \\\\ \\hline &&&\\dfrac{-7y}{-7}&=&\\dfrac{-28}{-7} \\\\ \\\\ &&&y&=&4 \\\\ \\\\ &4x&+&2(4)&=&0 \\\\ &4x&+&8&=&0 \\\\ &&-&8&&-8 \\\\ \\hline &&&\\dfrac{4x}{4}&=&\\dfrac{-8}{4} \\\\ \\\\ &&&x&=&-2 \\\\ (-2,4)&&&&& \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrcrr} &-7x&+&y&=&-10 \\\\ +&-9x&-&y&=&-22 \\\\ \\hline &&&\\dfrac{-16x}{-16}&=&\\dfrac{-32}{-16} \\\\ \\\\ &&&x&=&2 \\\\ \\\\ &-7(2)&+&y&=&-10 \\\\ &-14&+&y&=&-10 \\\\ &+14&&&&+14 \\\\ \\hline &&&y&=&4 \\\\ (2,4)&&&&& \\end{array}[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &-9x&+&5y&=&-22 \\\\ +&9x&-&5y&=&13 \\\\ \\hline &&&0&=&-9 \\end{array}\\\\ \\therefore \\text{Two parallel lines. No solution}[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &-x&-&2y&=&-7 \\\\ +&x&+&2y&=&7 \\\\ \\hline &&&0&=&0\\\\ \\end{array}\\\\ \\therefore \\text{Two identical lines. Infinite solutions}[\/latex]<\/li>\n
    5. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &-6x&+&9y&=&3 \\\\ +&6x&-&9y&=&-9 \\\\ \\hline &&&0&=&-6 \\end{array}\\\\ \\therefore \\text{Two parallel lines. No solution}[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &5x&-&5y&=&-15&(\\div 5) \\\\ &(x&-&y&=&-3)&(-1) \\\\ \\\\ &x&-&y&=&-3& \\\\ +&-x&+&y&=&3& \\\\ \\hline &&&0&=&0& \\\\ \\end{array}\\\\ \\therefore \\text{Two identical lines. Infinite solutions}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &4x&-&6y&=&-10 \\\\ +&4x&+&6y&=&-14 \\\\ \\hline &&&\\dfrac{8x}{8}&=&\\dfrac{-24}{8} \\\\ \\\\ &&&x&=&-3 \\\\ \\\\ &4(-3)&-&6y&=&-10 \\\\ &-12&-&6y&=&-10 \\\\ &+12&&&&+12 \\\\ \\hline &&&\\dfrac{-6y}{-6}&=&\\dfrac{2}{-6} \\\\ \\\\ &&&y&=&-\\dfrac{1}{3} \\\\ (-3, -\\dfrac{1}{3})&&&&& \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrl} &-3x&+&3y&=&-12&\\div &(-3) \\\\ &-3x&+&9y&=&-24&\\div &(3) \\\\ \\\\ & x&-&y&=&4&& \\\\ +&-x&+&3y&=&-8&& \\\\ \\hline &&&\\dfrac{2y}{2}&=&\\dfrac{-4}{2}&& \\\\ \\\\ &&&y&=&-2&& \\\\ \\\\ &\\therefore x&-&y&=&4&& \\\\ &x&-&-2&=&4&& \\\\ &x&+&2&=&4&& \\\\ &&-&2&&-2&& \\\\ \\hline &&&x&=&2&& \\\\ (2,-2)&&&&&&& \\end{array}[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &(-x&-&5y&=&28)&(-1) \\\\ \\\\ &x&+&5y&=&-28& \\\\ +&-x&+&4y&=&-17& \\\\ \\hline &&&\\dfrac{9y}{9}&=&\\dfrac{-45}{9}& \\\\ \\\\ &&&y&=&-5& \\\\ \\\\ &x&+&5(-5)&=&-28& \\\\ &x&-&25&=&-28& \\\\ &&+&25&&+25& \\\\ \\hline &&&x&=&-3& \\\\ (-3,-5)&&&&&& \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &(-10x&-&5y&=&0)&(-1) \\\\ \\\\ &10x&+&5y&=&0& \\\\ +&-10x&-&10y&=&-30& \\\\ \\hline &&&\\dfrac{-5y}{-5}&=&\\dfrac{-30}{-5}& \\\\ \\\\ &&&y&=&6& \\\\ \\\\ &10x&+&5(6)&=&0& \\\\ &10x&+&30&=&0& \\\\ &&-&30&&-30& \\\\ \\hline &&&\\dfrac{10x}{10}&=&\\dfrac{-30}{10}& \\\\ \\\\ &&&x&=&-3& \\\\ (-3,6)&&&&&& \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &(2x&-&y&=&5)&(2) \\\\ \\\\ &4x&-&2y&=&10& \\\\ +&5x&+&2y&=&-28& \\\\ \\hline &&&\\dfrac{9x}{9}&=&\\dfrac{-18}{9}& \\\\ \\\\ &&&x&=&-2& \\\\ \\\\ &2(x)&-&y&=&5& \\\\ &2(-2)&-&y&=&5& \\\\ &-4&-&y&=&5& \\\\ &+4&&&&+4& \\\\ \\hline &&&-y&=&9& \\\\ \\\\ &&&y&=&-9& \\\\ (-2,-9)&&&&&& \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &-5x&+&6y&=&-17& \\\\ &(x&-&2y&=&5)&(3) \\\\ \\\\ &-5x&+&6y&=&-17& \\\\ +&3x&-&6y&=&15& \\\\ \\hline &&&\\dfrac{-2x}{-2}&=&\\dfrac{-2}{-2}& \\\\ \\\\ &&&x&=&1& \\\\ \\\\ &x&-&2y&=&5& \\\\ &1&-&2y&=&5& \\\\ &-1&&&&-1& \\\\ \\hline &&&\\dfrac{-2y}{-2}&=&\\dfrac{4}{-2}& \\\\ \\\\ &&&y&=&-2& \\\\ (1,-2)&&&&&& \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &(10x&+&6y&=&24)&(\\div 2) \\\\ &(-6x&+&y&=&4)&(-3) \\\\ \\\\ &5x&+&3y&=&12& \\\\ +&18x&-&3y&=&-12& \\\\ \\hline &&&23x&=&0& \\\\ &&&x&=&0& \\\\ \\\\ &-6(x)&+&y&=&4& \\\\ &-6(0)&+&y&=&4& \\\\ &&&y&=&4& \\\\ (0,4)&&&&&& \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &(10x&+&6y&=&-10)&(\\div -2) \\\\ \\\\ &x&+&3y&=&-1& \\\\ +&-5x&-&3y&=&5& \\\\ \\hline &&&\\dfrac{-4x}{-4}&=&\\dfrac{4}{-4}& \\\\ \\\\ &&&x&=&-1& \\\\ \\\\ &-1&+&3y&=&-1& \\\\ &+1&&&&+1& \\\\ \\hline &&&3y&=&0& \\\\ \\\\ &&&y&=&0& \\\\ (-1,0)&&&&&& \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} &(2x&+&4y&=&24)&(\\div 2) \\\\ &(4x&-&12y&=&8)&(\\div -4) \\\\ \\\\ &x&+&2y&=&12& \\\\ +&-x&+&3y&=&-2& \\\\ \\hline &&&\\dfrac{5y}{5}&=&\\dfrac{10}{5}& \\\\ \\\\ &&&y&=&2& \\\\ \\\\ &x&+&2(y)&=&12& \\\\ &x&+&2(2)&=&12& \\\\ &x&+&4&=&12& \\\\ &&-&4&&-4& \\\\ \\hline &&&x&=&8& \\\\ (8,2)&&&&&& \\end{array}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} &(-6x&+&4y&=&12)&(\\div 2) \\\\ &(12x&+&6y&=&18)&(\\div -3) \\\\ \\\\ &-3x&+&2y&=&6& \\\\ +&-4x&-&2y&=&-6& \\\\ \\hline &&&-7x&=&0& \\\\ &&&x&=&0& \\\\ \\\\ &\\dfrac{-3(x)}{2}&+&\\dfrac{2y}{2}&=&\\dfrac{6}{2}& \\\\ \\\\ &\\dfrac{-3(0)}{2}&+&\\dfrac{2y}{2}&=&\\dfrac{6}{2}& \\\\ \\\\ &&&y&=&3& \\\\ (0,3)&&&&&& \\end{array}[\/latex]<\/li>\n
    17. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &(10x&-&8y&=&-8)&(\\div 2) \\\\ \\\\ &-7x&+&4y&=&-4& \\\\ +&5x&-&4y&=&-4& \\\\ \\hline &&&\\dfrac{-2x}{-2}&=&\\dfrac{-8}{-2}& \\\\ \\\\ &&&x&=&4& \\\\ \\\\ &5(4)&-&4y&=&-4& \\\\ &20&-&4y&=&-4& \\\\ &-20&&&&-20& \\\\ \\hline &&&\\dfrac{-4y}{-4}&=&\\dfrac{-24}{-4}& \\\\ \\\\ &&&y&=&6& \\\\ (4,6)&&&&&& \\end{array}[\/latex]<\/li>\n
    18. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &(-6x&+&4y&=&4)&(\\div 2) \\\\ \\\\ &-3x&+&2y&=&2& \\\\ +&3x&-&y&=&26& \\\\ \\hline &&&y&=&28& \\\\ \\\\ &3x&-&28&=&26& \\\\ &&+&28&&+28& \\\\ \\hline &&&\\dfrac{3x}{3}&=&\\dfrac{54}{3}& \\\\ \\\\ &&&x&=&18& \\\\ (18,28)&&&&&& \\end{array}[\/latex]<\/li>\n
    19. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &(-6x&-&5y&=&-3)&(2) \\\\ \\\\ &5x&+&10y&=&20& \\\\ +&-12x&-&10y&=&-6& \\\\ \\hline &&&\\dfrac{-7x}{-7}&=&\\dfrac{14}{-7}& \\\\ \\\\ &&&x&=&-2& \\\\ \\\\ &5(-2)&+&10y&=&20& \\\\ &-10&+&10y&=&20& \\\\ &+10&&&&+10& \\\\ \\hline &&&\\dfrac{10y}{10}&=&\\dfrac{30}{10}& \\\\ \\\\ &&&y&=&3& \\\\ (-2,3)&&&&&& \\end{array}[\/latex]<\/li>\n
    20. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} &(3x&-&7y&=&-11)&(3) \\\\ \\\\ &-9x&-&5y&=&-19& \\\\ +&9x&-&21y&=&-33& \\\\ \\hline &&&\\dfrac{-26y}{-26}&=&\\dfrac{-52}{-26}& \\\\ \\\\ &&&y&=&2& \\\\ \\\\ &3x&-&7(2)&=&-11& \\\\ &3x&-&14&=&-11& \\\\ &&+&14&&+14& \\\\ \\hline &&&\\dfrac{3x}{3}&=&\\dfrac{3}{3}& \\\\ \\\\ &&&x&=&1& \\\\ (1,2)&&&&&& \\end{array}[\/latex]<\/li>\n
    21. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} &(-7x&+&5y&=&-8)&(3) \\\\ &(-3x&-&3y&=&12)&(5) \\\\ \\\\ &-21x&+&15y&=&-24& \\\\ +&-15x&-&15y&=&60& \\\\ \\hline &&&\\dfrac{-36x}{-36}&=&\\dfrac{36}{-36}& \\\\ \\\\ &&&x&=&-1& \\\\ \\\\ &-3(-1)&-&3y&=&12& \\\\ &3&-&3y&=&12& \\\\ &-3&&&&-3& \\\\ \\hline &&&\\dfrac{-3y}{-3}&=&\\dfrac{9}{-3}& \\\\ \\\\ &&&y&=&-3& \\\\ (-1,-3)&&&&&& \\end{array}[\/latex]<\/li>\n
    22. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrcll} &&(6x&+&3y&=&-18)&\\div &-3 \\\\ \\\\ &&-2x&-&y&=&6&& \\\\ &&+2x&&&&+2x&& \\\\ \\hline &&&&-y&=&2x&+&6 \\\\ &&&&y&=&-2x&-&6 \\\\ \\\\ 8x&+&7(-2x&-&6)&=&-24&& \\\\ 8x&-&14x&-&42&=&-24&& \\\\ &&&+&42&&+42&& \\\\ \\hline &&&&\\dfrac{-6x}{-6}&=&\\dfrac{18}{-6}&& \\\\ \\\\ &&&&x&=&-3&& \\\\ \\\\ &&&&y&=&-2(-3)&-&6 \\\\ &&&&y&=&6&-&6 \\\\ &&&&y&=&0&& \\\\ (-3,0)&&&&&&&& \\\\ \\end{array}[\/latex]<\/li>\n
    23. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} &&(-8x&-&8y&=&-8)&\\div &(-8) \\\\ \\\\ &&x&+&y&=&1&& \\\\ &&-x&&&&-x&& \\\\ \\hline &&&&y&=&1&-&x \\\\ \\\\ 10x&+&9(1&-&x)&=&1&& \\\\ 10x&+&9&-&9x&=&1&& \\\\ &-&9&&&&-9&& \\\\ \\hline &&&&x&=&-8&& \\\\ \\\\ &&&&y&=&1&-&-8 \\\\ &&&&y&=&9&& \\\\ (-8,9)&&&&&&&& \\end{array}[\/latex]<\/li>\n
    24. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrl} &(-7x&+&10y&=&13)&(4) \\\\ &(4x&+&9y&=&22)&(7) \\\\ \\\\ &-28x&+&40y&=&52& \\\\ +&28x&+&63y&=&154& \\\\ \\hline &&&\\dfrac{103y}{103}&=&\\dfrac{206}{103}& \\\\ \\\\ &&&y&=&2& \\\\ \\\\ &4x&+&9(2)&=&22& \\\\ &4x&+&18&=&22& \\\\ &&-&18&&-18& \\\\ \\hline &&&\\dfrac{4x}{4}&=&\\dfrac{4}{4}& \\\\ \\\\ &&&x&=&1& \\\\ (1,2)&&&&&& \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":44,"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-1853","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\/1853","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\/1853\/revisions"}],"predecessor-version":[{"id":1854,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1853\/revisions\/1854"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1853\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1853"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1853"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1853"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1853"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}