{"id":1510,"date":"2019-06-27T12:40:50","date_gmt":"2019-06-27T16:40:50","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1510"},"modified":"2019-06-27T17:52:04","modified_gmt":"2019-06-27T21:52:04","slug":"answer-key-5-4","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-5-4\/","title":{"raw":"Answer Key 5.4","rendered":"Answer Key 5.4"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n\\\\\r\n&a&-&b&+&2c&=&2& \\\\\r\n+&a&+&b&+&c&=&3& \\\\\r\n\\midrule\r\n&&&2a&+&3c&=&5& \\\\ \\\\\r\n&a&-&b&+&2c&=&2& \\\\\r\n+&2a&+&b&-&c&=&2& \\\\\r\n\\midrule\r\n&&&(3a&+&c&=&4)&(-3) \\\\\r\n&&&-9a&-&3c&=&-12& \\\\ \\\\\r\n&&&-9a&-&3c&=&-12& \\\\\r\n+&&&2a&+&3c&=&5& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{-7a}{-7}&=&\\dfrac{-7}{-7}& \\\\ \\\\\r\n&&&&&a&=&1&\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrrrrl}\r\n&&3a&+&c&=&4& \\\\\r\n&&3(1)&+&c&=&4& \\\\\r\n&&3&+&c&=&4& \\\\\r\n&&-3&&&&-3& \\\\\r\n\\midrule\r\n&&&&c&=&1& \\\\ \\\\\r\na&+&b&+&c&=&3& \\\\\r\n(1)&+&b&+&(1)&=&3& \\\\\r\n&&b&+&2&=&3& \\\\\r\n&&&-&2&&-2& \\\\\r\n\\midrule\r\n&&&&b&=&1&\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n\\\\ \\\\\r\n&2a&+&3b&-&c&=&12& \\\\\r\n+&3a&+&4b&+&c&=&19& \\\\\r\n\\midrule\r\n&&&5a&+&7b&=&31& \\\\ \\\\\r\n&2a&+&3b&-&c&=&12& \\\\\r\n+&a&-&2b&+&c&=&-3& \\\\\r\n\\midrule\r\n&&&(3a&+&b&=&9)&(-7) \\\\\r\n&&&-21a&-&7b&=&-63& \\\\ \\\\\r\n&&&5a&+&7b&=&31& \\\\\r\n+&&&-21a&-&7b&=&-63& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{-16a}{-16}&=&\\dfrac{-32}{-16}& \\\\ \\\\\r\n&&&&&a&=&2&\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrrrr}\r\n&&3a&+&b&=&9 \\\\\r\n&&3(2)&+&b&=&9 \\\\\r\n&&6&+&b&=&9 \\\\\r\n&&-6&&&&-6 \\\\\r\n\\midrule\r\n&&&&b&=&3 \\\\ \\\\\r\na&-&2b&+&c&=&-3 \\\\\r\n(2)&-&2(3)&+&c&=&-3 \\\\\r\n2&-&6&+&c&=&-3 \\\\\r\n&&-4&+&c&=&-3 \\\\\r\n&&+4&&&&+4 \\\\\r\n\\midrule\r\n&&&&c&=&1\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&(3x&+&y&-&z&=&7)&(-1) \\\\\r\n&-3x&-&y&+&z&=&-7& \\\\\r\n+&x&+&3y&-&z&=&5& \\\\\r\n\\midrule\r\n&&&(-2x&+&2y&=&-2)&(\\div 2) \\\\\r\n&&&(-x&+&y&=&-1)&(7) \\\\\r\n&&&-7x&+&7y&=&-7& \\\\ \\\\\r\n&(3x&+&y&-&z&=&7)&(2) \\\\\r\n&6x&+&2y&-&2z&=&14& \\\\\r\n+&x&+&y&+&2z&=&3& \\\\\r\n\\midrule\r\n&&&7x&+&3y&=&17& \\\\\r\n+&&&-7x&+&7y&=&-7& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{10y}{10}&=&\\dfrac{10}{10}& \\\\ \\\\\r\n&&&&&y&=&1& \\\\\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrrrr}\r\n\\\\ \\\\\r\n&&-x&+&y&=&-1 \\\\\r\n&&-x&+&(1)&=&-1 \\\\\r\n&&-x&+&1&=&-1 \\\\\r\n&&&-&1&&-1 \\\\\r\n\\midrule\r\n&&&&-x&=&-2 \\\\\r\n&&&&x&=&2 \\\\ \\\\\r\nx&+&y&+&2z&=&3 \\\\\r\n(2)&+&(1)&+&2z&=&3 \\\\\r\n&&2z&+&3&=&3 \\\\\r\n&&&-&3&&-3 \\\\\r\n\\midrule\r\n&&&&2z&=&0 \\\\\r\n&&&&z&=&0 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&x&+&y&+&z&=&4&(-1) \\\\\r\n&-x&-&y&-&z&=&-4& \\\\ \\\\\r\n&-x&-&y&-&z&=&-4& \\\\\r\n+&x&+&2y&+&3z&=&10& \\\\\r\n\\midrule\r\n&&&(y&+&2z&=&6)&(2) \\\\\r\n&&&2y&+&4z&=&12& \\\\ \\\\\r\n&-x&-&y&-&z&=&-4& \\\\\r\n+&x&-&y&+&4z&=&20& \\\\\r\n\\midrule\r\n&&&-2y&+&3z&=&16& \\\\\r\n+&&&2y&+&4z&=&12& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{7z}{7}&=&\\dfrac{28}{7}& \\\\ \\\\\r\n&&&&&z&=&4&\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrr}\r\n&&y&+&2z&=&6 \\\\\r\n&&y&+&2(4)&=&6 \\\\\r\n&&y&+&8&=&6 \\\\\r\n&&&-&8&&-8 \\\\\r\n\\midrule\r\n&&&&y&=&-2 \\\\ \\\\\r\nx&+&y&+&z&=&4 \\\\\r\nx&+&(-2)&+&(4)&=&4 \\\\\r\n&&x&+&2&=&4 \\\\\r\n&&&-&2&&-2 \\\\\r\n\\midrule\r\n&&&&x&=&2\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&x&+&2y&-&z&=&0& \\\\\r\n+&3x&-&2y&-&4z&=&-5& \\\\\r\n\\midrule\r\n&&&4x&-&5z&=&-5& \\\\ \\\\\r\n&(2x&-&y&+&z&=&15)&(2) \\\\\r\n&4x&-&2y&+&2z&=&30& \\\\\r\n+&x&+&2y&-&z&=&0& \\\\\r\n\\midrule\r\n&&&(5x&+&z&=&30)&(5) \\\\\r\n&&&25x&+&5z&=&150& \\\\ \\\\\r\n&&&4x&-&5z&=&-5& \\\\\r\n+&&&25x&+&5z&=&150& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{29x}{29}&=&\\dfrac{145}{29}& \\\\ \\\\\r\n&&&&&x&=&5& \\\\\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrr}\r\n&&5x&+&z&=&30 \\\\\r\n&&5(5)&+&z&=&30 \\\\\r\n&&25&+&z&=&30 \\\\\r\n&&-25&&&&-25 \\\\\r\n\\midrule\r\n&&&&z&=&5 \\\\ \\\\\r\nx&+&2y&-&z&=&0 \\\\\r\n(5)&+&2y&-&(5)&=&0 \\\\\r\n5&+&2y&-&5&=&0 \\\\\r\n&&&&2y&=&0 \\\\\r\n&&&&y&=&0 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&(x&-&y&+&2z&=&-3)&(2) \\\\\r\n&2x&-&2y&+&4z&=&-6& \\\\\r\n+&x&+&2y&+&3z&=&4& \\\\\r\n\\midrule\r\n&&&(3x&+&7z&=&-2)&(-1) \\\\\r\n&&&-3x&-&7z&=&2& \\\\ \\\\\r\n&2x&+&y&+&z&=&-3& \\\\\r\n+&x&-&y&+&2z&=&-3& \\\\\r\n\\midrule\r\n&&&3x&+&3z&=&-6& \\\\\r\n+&&&-3x&-&7z&=&2& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{-4z}{-4}&=&\\dfrac{-4}{-4}& \\\\ \\\\\r\n&&&&&z&=&1& \\\\\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrrrr}\r\n&&3x&+&3z&=&-6 \\\\\r\n&&3x&+&3(1)&=&-6 \\\\\r\n&&3x&+&3&=&-6 \\\\\r\n&&&-&3&&-3 \\\\\r\n\\midrule\r\n&&&&\\dfrac{3x}{3}&=&\\dfrac{-9}{3} \\\\ \\\\\r\n&&&&x&=&-3 \\\\ \\\\\r\nx&-&y&+&2z&=&-3 \\\\\r\n(-3)&-&y&+&2(1)&=&-3 \\\\\r\n-3&-&y&+&2&=&-3 \\\\\r\n&&-y&-&1&=&-3 \\\\\r\n&&&+&1&&+1 \\\\\r\n\\midrule\r\n&&&&-y&=&-2 \\\\\r\n&&&&y&=&2\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n\\\\\r\n&x&+&y&+&z&=&6& \\\\\r\n+&2x&-&y&-&z&=&-3& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{3x}{3}&=&\\dfrac{3}{3}& \\\\ \\\\\r\n&&&&&x&=&1& \\\\ \\\\\r\n&x&-&2y&+&3z&=&6& \\\\\r\n&(1)&-&2y&+&3z&=&6& \\\\\r\n&1&-&2y&+&3z&=&6& \\\\\r\n&-1&&&&&&-1& \\\\\r\n\\midrule\r\n&&&-2y&+&3z&=&5& \\\\ \\\\\r\n&x&+&y&+&z&=&6& \\\\\r\n&(1)&+&y&+&z&=&6& \\\\\r\n&1&+&y&+&z&=&6& \\\\\r\n&-1&&&&&&-1& \\\\\r\n\\midrule\r\n&&&(y&+&z&=&5)&(2) \\\\\r\n&&&2y&+&2z&=&10&\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&&-2y&+&3z&=&5 \\\\\r\n+&&2y&+&2z&=&10 \\\\\r\n\\midrule\r\n&&&&\\dfrac{5z}{5}&=&\\dfrac{15}{5} \\\\ \\\\\r\n&&&&z&=&3 \\\\ \\\\\r\nx&+&y&+&z&=&6 \\\\\r\n(1)&+&y&+&(3)&=&6 \\\\\r\n1&+&y&+&3&=&6 \\\\\r\n&&y&+&4&=&6 \\\\\r\n&&&-&4&&-4 \\\\\r\n\\midrule\r\n&&&&y&=&2 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&x&+&y&-&z&=&0& \\\\\r\n+&2x&+&y&+&z&=&0& \\\\\r\n\\midrule\r\n&&&3x&+&2y&=&0& \\\\ \\\\\r\n&(x&+&y&-&z&=&0)&(-4) \\\\\r\n&-4x&-&4y&+&4z&=&0& \\\\\r\n+&x&+&2y&-&4z&=&0& \\\\\r\n\\midrule\r\n&&&-3x&-&2y&=&0& \\\\\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrr}\r\n&-3x&-&2y&=&0 \\\\\r\n+&3x&+&2y&=&0 \\\\\r\n\\midrule\r\n&&&0&=&0 \\\\ \\\\\r\n&&\\therefore &x&=&0 \\\\\r\n&&&y&=&0 \\\\\r\n&&&z&=&0 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&x&+&y&+&z&=&2& \\\\\r\n+&2x&-&y&+&3z&=&9& \\\\\r\n\\midrule\r\n&&&3x&+&4z&=&11& \\\\ \\\\\r\n&2x&-&y&+&3z&=&9& \\\\\r\n+&&&y&-&z&=&-3& \\\\\r\n\\midrule\r\n&&&(2x&+&2z&=&6)&(-2) \\\\\r\n&&&-4x&-&4z&=&-12& \\\\ \\\\\r\n&&&3x&+&4z&=&11& \\\\\r\n+&&&-4x&-&4z&=&-12& \\\\\r\n\\midrule\r\n&&&&&-x&=&-1& \\\\\r\n&&&&&x&=&1&\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrr}\r\n&&2x&+&2z&=&6 \\\\\r\n&&2(1)&+&2z&=&6 \\\\\r\n&&2&+&2z&=&6 \\\\\r\n&&-2&&&&-2 \\\\\r\n\\midrule\r\n&&&&\\dfrac{2z}{2}&=&\\dfrac{4}{2} \\\\ \\\\\r\n&&&&z&=&2 \\\\ \\\\\r\nx&+&y&+&z&=&2 \\\\\r\n(1)&+&y&+&(2)&=&2 \\\\\r\n&&y&+&3&=&2 \\\\\r\n&&&-&3&&-3 \\\\\r\n\\midrule\r\n&&&&y&=&-1 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&(4x&&&+&z&=&3)&(2) \\\\\r\n&8x&&&+&2z&=&6& \\\\\r\n+&6x&-&y&-&2z&=&-1& \\\\\r\n\\midrule\r\n&&&(14x&-&y&=&5)&(3) \\\\\r\n&&&42x&-&3y&=&15& \\\\\r\n+&&&-2x&+&3y&=&5& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{40x}{40}&=&\\dfrac{20}{40}& \\\\ \\\\\r\n&&&&&x&=&\\dfrac{1}{2}&\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&&-2x&+&3y&=&5 \\\\\r\n&&-2\\left(\\dfrac{1}{2}\\right)&+&3y&=&5 \\\\\r\n&&-1&+&3y&=&5 \\\\\r\n&&+1&&&&+1 \\\\\r\n\\midrule\r\n&&&&\\dfrac{3y}{3}&=&\\dfrac{6}{3} \\\\ \\\\\r\n&&&&y&=&2 \\\\ \\\\\r\n&&4x&+&z&=&3 \\\\\r\n&&4\\left(\\dfrac{1}{2}\\right)&+&z&=&3 \\\\\r\n&&2&+&z&=&3 \\\\\r\n&&-2&&&&-2 \\\\\r\n\\midrule\r\n&&&&z&=&1 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&&&x&-&z&=&-2& \\\\\r\n+&&&y&+&z&=&5& \\\\\r\n\\midrule\r\n&&&x&+&y&=&3& \\\\ \\\\\r\n&2x&-&3y&+&z&=&-1& \\\\\r\n+&x&&&-&z&=&-2& \\\\\r\n\\midrule\r\n&&&(3x&-&3y&=&-3)&(\\div 3) \\\\\r\n&&&x&-&y&=&-1& \\\\\r\n+&&&x&+&y&=&3& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{2x}{2}&=&\\dfrac{2}{2}& \\\\ \\\\\r\n&&&&&x&=&1&\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\nx&-&z&=&-2 \\\\\r\n(1)&-&z&=&-2 \\\\\r\n1&-&z&=&-2 \\\\\r\n-1&&&&-1 \\\\\r\n\\midrule\r\n&&-z&=&-3 \\\\\r\n&&z&=&3 \\\\ \\\\\r\ny&+&z&=&5 \\\\\r\ny&+&(3)&=&5 \\\\\r\ny&+&3&=&5 \\\\\r\n&-&3&&-3 \\\\\r\n\\midrule\r\n&&y&=&2 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&(3x&+&4y&-&z&=&11)&(2) \\\\\r\n&6x&+&8y&-&2z&=&22& \\\\\r\n+&&&y&+&2z&=&-4& \\\\\r\n\\midrule\r\n&&&(6x&+&9y&=&18)&(\\div 3) \\\\\r\n&&&2x&+&3y&=&6& \\\\\r\n+&&&-2x&+&y&=&-6& \\\\\r\n\\midrule\r\n&&&&&4y&=&0& \\\\\r\n&&&&&y&=&0& \\\\ \\\\\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\\r\n-2x&+&y&=&-6 \\\\\r\n-2x&+&0&=&-6 \\\\\r\n&&\\dfrac{-2x}{-2}&=&\\dfrac{-6}{-2} \\\\ \\\\\r\n&&x&=&3 \\\\ \\\\\r\ny&+&2z&=&-4 \\\\\r\n0&+&2z&=&-4 \\\\\r\n&&\\dfrac{2z}{2}&=&\\dfrac{-4}{2} \\\\ \\\\\r\n&&z&=&-2\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&&&(-2y&+&z&=&-6)&(3) \\\\\r\n&&&-6y&+&3z&=&-18& \\\\\r\n+&x&+&6y&+&3z&=&30& \\\\\r\n\\midrule\r\n&&&(x&+&6z&=&12)&(-2) \\\\\r\n&&&-2x&-&12z&=&-24& \\\\\r\n+&&&2x&+&2z&=&4& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{-10z}{-10}&=&\\dfrac{-20}{-10}& \\\\ \\\\\r\n&&&&&z&=&2&\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\\r\n2x&+&2z&=&4 \\\\\r\n2x&+&2(2)&=&4 \\\\\r\n2x&+&4&=&4 \\\\\r\n&-&4&&-4 \\\\\r\n\\midrule\r\n&&2x&=&0 \\\\\r\n&&x&=&0 \\\\ \\\\\r\n-2y&+&z&=&-6 \\\\\r\n-2y&+&2&=&-6 \\\\\r\n&-&2&&-2 \\\\\r\n\\midrule\r\n&&\\dfrac{-2y}{-2}&=&\\dfrac{-8}{-2} \\\\ \\\\\r\n&&y&=&4\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&(x&-&y&+&2z&=&0)&(2) \\\\\r\n&2x&-&2y&+&4z&=&0& \\\\\r\n+&x&+&2y&&&=&1& \\\\\r\n\\midrule\r\n&&&3x&+&4z&=&1& \\\\ \\\\\r\n&&&(2x&+&z&=&4)&(-4) \\\\\r\n&&&-8x&-&4z&=&-16& \\\\\r\n+&&&3x&+&4z&=&1& \\\\\r\n\\midrule\r\n&&&&&\\dfrac{-5x}{-5}&=&\\dfrac{-15}{-5}& \\\\ \\\\\r\n&&&&&x&=&3&\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\nx&+&2y&=&1 \\\\\r\n3&+&2y&=&1 \\\\\r\n-3&&&&-3 \\\\\r\n\\midrule\r\n&&\\dfrac{2y}{2}&=&\\dfrac{-2}{2} \\\\ \\\\\r\n&&y&=&-1 \\\\ \\\\\r\n2x&+&z&=&4 \\\\\r\n2(3)&+&z&=&4 \\\\\r\n6&+&z&=&4 \\\\\r\n-6&&&&-6 \\\\\r\n\\midrule\r\n&&z&=&-2\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rr}\r\n\\\\ \\\\\r\n\\begin{array}{rrrrrrrr}\r\n&x&+&y&+&z&=&4 \\\\\r\n+&&-&y&-&z&=&-4 \\\\\r\n\\midrule\r\n&&&&&x&=&0\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx&-&2y&=&0 \\\\\r\n0&-&2y&=&0 \\\\\r\n&&-2y&=&0 \\\\\r\n&&y&=&0 \\\\ \\\\\r\n-y&-&z&=&-4 \\\\\r\n0&-&z&=&-4 \\\\\r\n&&-z&=&-4 \\\\\r\n&&z&=&4\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n&(x&+&y&-&z&=&2)&(-2) \\\\\r\n&-2x&-&2y&+&2z&=&-4& \\\\\r\n+&2x&&&+&z&=&6& \\\\\r\n\\midrule\r\n&&&-2y&+&3z&=&2& \\\\\r\n+&&&2y&-&4z&=&-4& \\\\\r\n\\midrule\r\n&&&&&-z&=&-2& \\\\\r\n&&&&&z&=&2&\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2x&+&z&=&6 \\\\\r\n2x&+&2&=&6 \\\\\r\n&-&2&&-2 \\\\\r\n\\midrule\r\n&&\\dfrac{2x}{2}&=&\\dfrac{4}{2} \\\\ \\\\\r\n&&x&=&2 \\\\ \\\\\r\n2y&-&4z&=&-4 \\\\\r\n2y&-&4(2)&=&-4 \\\\\r\n2y&-&8&=&-4 \\\\\r\n&+&8&&+8 \\\\\r\n\\midrule\r\n&&\\dfrac{2y}{2}&=&\\dfrac{4}{2} \\\\ \\\\\r\n&&y&=&2\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
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    14. \"\begin{array}{rr}<\/li>\n
    15. \"\begin{array}{rr}<\/li>\n
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