{"id":1488,"date":"2019-06-25T19:00:33","date_gmt":"2019-06-25T23:00:33","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1488"},"modified":"2019-10-25T16:48:47","modified_gmt":"2019-10-25T20:48:47","slug":"answer-key-5-2","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-5-2\/","title":{"raw":"Answer Key 5.2","rendered":"Answer Key 5.2"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-3x&=&6x&-&9 \\\\\r\n-6x&&-6x&& \\\\\r\n\\midrule\r\n\\dfrac{-9x}{-9}&=&\\dfrac{-9}{-9}&& \\\\ \\\\\r\nx&=&1&& \\\\ \\\\\r\n\\therefore y&=&-3(1)&& \\\\\r\ny&=&-3&& \\\\ \\\\\r\n(1,-3)&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx&+&5&=&-2x&-&4 \\\\\r\n+2x&-&5&&+2x&-&5 \\\\\r\n\\midrule\r\n&&\\dfrac{3x}{3}&=&\\dfrac{-9}{3}&& \\\\ \\\\\r\n&&x&=&-3&& \\\\ \\\\\r\n&&\\therefore y&=&-3&+&5 \\\\\r\n&&y&=&2&& \\\\ \\\\\r\n(-3,2)&&&&&& \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2x&-&1&=&-2x&-&9 \\\\\r\n+2x&+&1&&+2x&+&1 \\\\\r\n\\midrule\r\n&&\\dfrac{4x}{4}&=&\\dfrac{-8}{4}&& \\\\ \\\\\r\n&&x&=&-2&& \\\\ \\\\\r\n&&\\therefore y&=&2(-2)&-&1 \\\\\r\n&&y&=&-4&-&1 \\\\\r\n&&y&=&-5&& \\\\\r\n(-2,-5)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n6x&+&3&=&-6x&+&3 \\\\\r\n+6x&-&3&&+6x&-&3 \\\\\r\n\\midrule\r\n&&\\dfrac{12x}{12}&=&\\dfrac{0}{12}&& \\\\ \\\\\r\n&&x&=&0&& \\\\ \\\\\r\n&&\\therefore y&=&6(0)&+&3 \\\\\r\n&&y&=&3&& \\\\\r\n(0,3)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n6x&+&4&=&-3x&-&5 \\\\\r\n+3x&-&4&&+3x&-&4 \\\\\r\n\\midrule\r\n&&\\dfrac{9x}{9}&=&\\dfrac{-9}{9}&& \\\\ \\\\\r\n&&x&=&-1&& \\\\ \\\\\r\n&&\\therefore y&=&6(-1)&+&4 \\\\\r\n&&y&=&-6&+&4 \\\\\r\n&&y&=&-2&& \\\\\r\n(-1,-2)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n3x&+&13&=&-2x&-&22 \\\\\r\n+2x&-&13&&+2x&-&13 \\\\\r\n\\midrule\r\n&&\\dfrac{5x}{5}&=&\\dfrac{-35}{5}&& \\\\ \\\\\r\n&&x&=&-7&& \\\\ \\\\\r\n&&\\therefore y&=&3(-7)&+&13 \\\\\r\n&&y&=&-21&+&13 \\\\\r\n&&y&=&-8&& \\\\\r\n(-7,-8)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n3x&+&2&=&-3x&+&8 \\\\\r\n+3x&-&2&&+3x&-&2 \\\\\r\n\\midrule\r\n&&\\dfrac{6x}{6}&=&\\dfrac{6}{6}&& \\\\ \\\\\r\n&&x&=&1&& \\\\ \\\\\r\n&&\\therefore y&=&3(1)&+&2 \\\\\r\n&&y&=&3&+&2 \\\\\r\n&&y&=&5&& \\\\\r\n(1,5)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-2x&-&9&=&-5x&-&21 \\\\\r\n+5x&+&9&&+5x&+&9 \\\\\r\n\\midrule\r\n&&\\dfrac{3x}{3}&=&\\dfrac{-12}{3}&& \\\\ \\\\\r\n&&x&=&-4&& \\\\ \\\\\r\n&&\\therefore y&=&-2(-4)&-&9 \\\\\r\n&&y&=&8&-&9 \\\\\r\n&&y&=&-1&& \\\\\r\n(-4,-1)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2x&-&3&=&-2x&+&9 \\\\\r\n+2x&+&3&&+2x&+&3 \\\\\r\n\\midrule\r\n&&\\dfrac{4x}{4}&=&\\dfrac{12}{4}&& \\\\ \\\\\r\n&&x&=&3&& \\\\ \\\\\r\n&&\\therefore y&=&2(3)&-&3 \\\\\r\n&&y&=&6&-&3 \\\\\r\n&&y&=&3&& \\\\\r\n(3,3)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n7x&-&24&=&-3x&+&16 \\\\\r\n+3x&+&24&&+3x&+&24 \\\\\r\n\\midrule\r\n&&\\dfrac{10x}{10}&=&\\dfrac{40}{10}&& \\\\ \\\\\r\n&&x&=&4&& \\\\ \\\\\r\n&&\\therefore y&=&7(4)&-&24 \\\\\r\n&&y&=&28&-&24 \\\\\r\n&&y&=&4&& \\\\\r\n(4,4)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n3x&-&3(3x&-&4)&=&-6 \\\\\r\n3x&-&9x&+&12&=&-6 \\\\\r\n&&&-&12&&-12 \\\\\r\n\\midrule\r\n&&&&\\dfrac{-6x}{-6}&=&\\dfrac{-18}{-6} \\\\ \\\\\r\n&&&&x&=&3 \\\\ \\\\\r\n&&&&\\therefore y&=&3(3)-4 \\\\\r\n&&&&y&=&9-4 \\\\\r\n&&&&y&=&5 \\\\\r\n(3,5)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-x&+&3(6x&+&21)&=&\\phantom{-}12 \\\\\r\n-x&+&18x&+&63&=&\\phantom{-}12 \\\\\r\n&&&-&63&&-63 \\\\\r\n\\midrule\r\n&&&&\\dfrac{17x}{17}&=&\\dfrac{-51}{17} \\\\ \\\\\r\n&&&&x&=&-3 \\\\ \\\\\r\n&&&&\\therefore y&=&6(-3)+21 \\\\\r\n&&&&y&=&-18+21 \\\\\r\n&&&&y&=&3 \\\\\r\n(-3,3)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n3x&-&6(-6)&=&30 \\\\\r\n3x&+&36&=&30 \\\\\r\n&-&36&&-36 \\\\\r\n\\midrule\r\n&&\\dfrac{3x}{3}&=&\\dfrac{-6}{3} \\\\ \\\\\r\n&&x&=&-2 \\\\ \\\\\r\n&&y&=&-6 \\\\\r\n(-2,-6)&&&& \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n6x&-&4(-6x&+&2)&=&-8 \\\\\r\n6x&+&24x&-&8&=&-8 \\\\\r\n&&&+&8&&+8 \\\\\r\n\\midrule\r\n&&&&\\dfrac{30x}{30}&=&\\dfrac{0}{30} \\\\ \\\\\r\n&&&&\\therefore x&=&0 \\\\ \\\\\r\n&&&&\\therefore y&=&-6(0)+2 \\\\\r\n&&&&y&=&0+2 \\\\\r\n&&&&y&=&2 \\\\\r\n(0,2)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n3x&+&4(-5)&=&-17 \\\\\r\n3x&-&20&=&-17 \\\\\r\n&+&20&&+20 \\\\\r\n\\midrule\r\n&&\\dfrac{3x}{3}&=&\\dfrac{3}{3} \\\\ \\\\\r\n&&x&=&1 \\\\ \\\\\r\n&&y&=&-5 \\\\\r\n(1,-5)&&&& \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n7x&+&2(5x&+&5)&=&-7 \\\\\r\n7x&+&10x&+&10&=&-7 \\\\\r\n&&&-&10&&-10 \\\\\r\n\\midrule\r\n&&&&\\dfrac{17x}{17}&=&\\dfrac{-17}{17} \\\\ \\\\\r\n&&&&x&=&-1 \\\\ \\\\\r\n&&&&\\therefore y&=&5(-1)+5 \\\\\r\n&&&&y&=&-5+5 \\\\\r\n&&&&y&=&0 \\\\\r\n(-1,0)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-6x&+&6y&=&-12&(\\div &6) \\\\\r\n-x&+&y&=&-2&& \\\\\r\n+x&&&&+x&& \\\\\r\n\\midrule\r\n&&y&=&x&-&2 \\\\ \\\\\r\n8x&-&3(x&-&2)&=&16 \\\\\r\n8x&-&3x&+&6&=&16 \\\\\r\n&&&-&6&&-6 \\\\\r\n\\midrule\r\n&&&&\\dfrac{5x}{5}&=&\\dfrac{10}{5} \\\\ \\\\\r\n&&&&x&=&2 \\\\ \\\\\r\n&&&&\\therefore y&=&x-2 \\\\\r\n&&&&y&=&2-2=0 \\\\\r\n(2,0)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-8x&+&2y&=&-6&(\\div &2) \\\\\r\n-4x&+&y&=&-3&& \\\\\r\n+4x&&&&+4x&& \\\\\r\n\\midrule\r\n&&y&=&4x&-&3 \\\\ \\\\\r\n-2x&+&3(4x&-&3)&=&11 \\\\\r\n-2x&+&12x&-&9&=&11 \\\\\r\n&&&+&9&&+9 \\\\\r\n\\midrule\r\n&&&&\\dfrac{10x}{10}&=&\\dfrac{20}{10} \\\\ \\\\\r\n&&&&x&=&2 \\\\ \\\\\r\n&&&&\\therefore y&=&4(2)-3 \\\\\r\n&&&&y&=&8-3=5 \\\\\r\n(2,5)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-7x&-&y&=&20&& \\\\\r\n-20&+&y&&-20&+&y \\\\\r\n\\midrule\r\n-7x&-&20&=&y&& \\\\ \\\\\r\n2x&+&3(-7x&-&20)&=&\\phantom{+}16 \\\\\r\n2x&-&21x&-&60&=&\\phantom{+}16 \\\\\r\n&&&+&60&&+60 \\\\\r\n\\midrule\r\n&&&&\\dfrac{-19x}{-19}&=&\\dfrac{76}{-19} \\\\ \\\\\r\n&&&&x&=&-4 \\\\ \\\\\r\n&&&&\\therefore y&=&-7(-4)-20 \\\\\r\n&&&&y&=&28-20 \\\\\r\n&&&&y&=&8 \\\\\r\n(-4,8)&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{rrrrrrrll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&(-x&-&4y&=&-14)&(-1)& \\\\\r\n&&x&+&4y&=&14&& \\\\\r\n&&&-&4y&&-4y&& \\\\\r\n\\midrule\r\n&&&&x&=&14&-&4y \\\\ \\\\\r\n&&(-6x&+&8y&=&12)&\\div &2 \\\\\r\n&&-3x&+&4y&=&6&& \\\\\r\n-3(14&-&4y)&+&4y&=&6&& \\\\\r\n-42&+&12y&+&4y&=&6&& \\\\\r\n+42&&&&&&+42&& \\\\\r\n\\midrule\r\n&&&&\\dfrac{16y}{16}&=&\\dfrac{48}{16}&& \\\\ \\\\\r\n&&&&y&=&3&& \\\\ \\\\\r\n&&&&x&=&14&-&4(3) \\\\\r\n&&&&x&=&14&-&12 \\\\\r\n&&&&x&=&2&& \\\\\r\n(2,3)&&&&&&&&\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
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