Answer Key 5.2

  1. \begin{array}{rrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ -3x&=&6x&-&9 \\ -6x&&-6x&& \\ \midrule \dfrac{-9x}{-9}&=&\dfrac{-9}{-9}&& \\ \\ x&=&1&& \\ \\ \therefore y&=&-3(1)&& \\ y&=&-3&& \\ \\ (1,-3)&&&& \end{array}
  2. \begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ x&+&5&=&-2x&-&4 \\ +2x&-&5&&+2x&-&5 \\ \midrule &&\dfrac{3x}{3}&=&\dfrac{-9}{3}&& \\ \\ &&x&=&-3&& \\ \\ &&\therefore y&=&-3&+&5 \\ &&y&=&2&& \\ \\ (-3,2)&&&&&& \\ \end{array}
  3. \begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 2x&-&1&=&-2x&-&9 \\ +2x&+&1&&+2x&+&1 \\ \midrule &&\dfrac{4x}{4}&=&\dfrac{-8}{4}&& \\ \\ &&x&=&-2&& \\ \\ &&\therefore y&=&2(-2)&-&1 \\ &&y&=&-4&-&1 \\ &&y&=&-5&& \\ (-2,-5)&&&&&& \end{array}
  4. \begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ 6x&+&3&=&-6x&+&3 \\ +6x&-&3&&+6x&-&3 \\ \midrule &&\dfrac{12x}{12}&=&\dfrac{0}{12}&& \\ \\ &&x&=&0&& \\ \\ &&\therefore y&=&6(0)&+&3 \\ &&y&=&3&& \\ (0,3)&&&&&& \end{array}
  5. \begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 6x&+&4&=&-3x&-&5 \\ +3x&-&4&&+3x&-&4 \\ \midrule &&\dfrac{9x}{9}&=&\dfrac{-9}{9}&& \\ \\ &&x&=&-1&& \\ \\ &&\therefore y&=&6(-1)&+&4 \\ &&y&=&-6&+&4 \\ &&y&=&-2&& \\ (-1,-2)&&&&&& \end{array}
  6. \begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 3x&+&13&=&-2x&-&22 \\ +2x&-&13&&+2x&-&13 \\ \midrule &&\dfrac{5x}{5}&=&\dfrac{-35}{5}&& \\ \\ &&x&=&-7&& \\ \\ &&\therefore y&=&3(-7)&+&13 \\ &&y&=&-21&+&13 \\ &&y&=&-8&& \\ (-7,-8)&&&&&& \end{array}
  7. \begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 3x&+&2&=&-3x&+&8 \\ +3x&-&2&&+3x&-&2 \\ \midrule &&\dfrac{6x}{6}&=&\dfrac{6}{6}&& \\ \\ &&x&=&1&& \\ \\ &&\therefore y&=&3(1)&+&2 \\ &&y&=&3&+&2 \\ &&y&=&5&& \\ (1,5)&&&&&& \end{array}
  8. \begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ -2x&-&9&=&-5x&-&21 \\ +5x&+&9&&+5x&+&9 \\ \midrule &&\dfrac{3x}{3}&=&\dfrac{-12}{3}&& \\ \\ &&x&=&-4&& \\ \\ &&\therefore y&=&-2(-4)&-&9 \\ &&y&=&8&-&9 \\ &&y&=&-1&& \\ (-4,-1)&&&&&& \end{array}
  9. \begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 2x&-&3&=&-2x&+&9 \\ +2x&+&3&&+2x&+&3 \\ \midrule &&\dfrac{4x}{4}&=&\dfrac{12}{4}&& \\ \\ &&x&=&3&& \\ \\ &&\therefore y&=&2(3)&-&3 \\ &&y&=&6&-&3 \\ &&y&=&3&& \\ (3,3)&&&&&& \end{array}
  10. \begin{array}{rrrrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 7x&-&24&=&-3x&+&16 \\ +3x&+&24&&+3x&+&24 \\ \midrule &&\dfrac{10x}{10}&=&\dfrac{40}{10}&& \\ \\ &&x&=&4&& \\ \\ &&\therefore y&=&7(4)&-&24 \\ &&y&=&28&-&24 \\ &&y&=&4&& \\ (4,4)&&&&&& \end{array}
  11. \begin{array}{rrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 3x&-&3(3x&-&4)&=&-6 \\ 3x&-&9x&+&12&=&-6 \\ &&&-&12&&-12 \\ \midrule &&&&\dfrac{-6x}{-6}&=&\dfrac{-18}{-6} \\ \\ &&&&x&=&3 \\ \\ &&&&\therefore y&=&3(3)-4 \\ &&&&y&=&9-4 \\ &&&&y&=&5 \\ (3,5)&&&&&& \end{array}
  12. \begin{array}{rrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ -x&+&3(6x&+&21)&=&\phantom{-}12 \\ -x&+&18x&+&63&=&\phantom{-}12 \\ &&&-&63&&-63 \\ \midrule &&&&\dfrac{17x}{17}&=&\dfrac{-51}{17} \\ \\ &&&&x&=&-3 \\ \\ &&&&\therefore y&=&6(-3)+21 \\ &&&&y&=&-18+21 \\ &&&&y&=&3 \\ (-3,3)&&&&&& \end{array}
  13. \begin{array}{rrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ 3x&-&6(-6)&=&30 \\ 3x&+&36&=&30 \\ &-&36&&-36 \\ \midrule &&\dfrac{3x}{3}&=&\dfrac{-6}{3} \\ \\ &&x&=&-2 \\ \\ &&y&=&-6 \\ (-2,-6)&&&& \\ \end{array}
  14. \begin{array}{rrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 6x&-&4(-6x&+&2)&=&-8 \\ 6x&+&24x&-&8&=&-8 \\ &&&+&8&&+8 \\ \midrule &&&&\dfrac{30x}{30}&=&\dfrac{0}{30} \\ \\ &&&&\therefore x&=&0 \\ \\ &&&&\therefore y&=&-6(0)+2 \\ &&&&y&=&0+2 \\ &&&&y&=&2 \\ (0,2)&&&&&& \end{array}
  15. \begin{array}{rrrrr} \\ \\ \\ \\ \\ \\ \\ \\ \\ 3x&+&4(-5)&=&-17 \\ 3x&-&20&=&-17 \\ &+&20&&+20 \\ \midrule &&\dfrac{3x}{3}&=&\dfrac{3}{3} \\ \\ &&x&=&1 \\ \\ &&y&=&-5 \\ (1,-5)&&&& \\ \end{array}
  16. \begin{array}{rrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 7x&+&2(5x&+&5)&=&-7 \\ 7x&+&10x&+&10&=&-7 \\ &&&-&10&&-10 \\ \midrule &&&&\dfrac{17x}{17}&=&\dfrac{-17}{17} \\ \\ &&&&x&=&-1 \\ \\ &&&&\therefore y&=&5(-1)+5 \\ &&&&y&=&-5+5 \\ &&&&y&=&0 \\ (-1,0)&&&&&& \end{array}
  17. \begin{array}{rrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ -6x&+&6y&=&-12&(\div &6) \\ -x&+&y&=&-2&& \\ +x&&&&+x&& \\ \midrule &&y&=&x&-&2 \\ \\ 8x&-&3(x&-&2)&=&16 \\ 8x&-&3x&+&6&=&16 \\ &&&-&6&&-6 \\ \midrule &&&&\dfrac{5x}{5}&=&\dfrac{10}{5} \\ \\ &&&&x&=&2 \\ \\ &&&&\therefore y&=&x-2 \\ &&&&y&=&2-2=0 \\ (2,0)&&&&&& \end{array}
  18. \begin{array}{rrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ -8x&+&2y&=&-6&(\div &2) \\ -4x&+&y&=&-3&& \\ +4x&&&&+4x&& \\ \midrule &&y&=&4x&-&3 \\ \\ -2x&+&3(4x&-&3)&=&11 \\ -2x&+&12x&-&9&=&11 \\ &&&+&9&&+9 \\ \midrule &&&&\dfrac{10x}{10}&=&\dfrac{20}{10} \\ \\ &&&&x&=&2 \\ \\ &&&&\therefore y&=&4(2)-3 \\ &&&&y&=&8-3=5 \\ (2,5)&&&&&& \end{array}
  19. \begin{array}{rrrrrrl} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ -7x&-&y&=&20&& \\ -20&+&y&&-20&+&y \\ \midrule -7x&-&20&=&y&& \\ \\ 2x&+&3(-7x&-&20)&=&\phantom{+}16 \\ 2x&-&21x&-&60&=&\phantom{+}16 \\ &&&+&60&&+60 \\ \midrule &&&&\dfrac{-19x}{-19}&=&\dfrac{76}{-19} \\ \\ &&&&x&=&-4 \\ \\ &&&&\therefore y&=&-7(-4)-20 \\ &&&&y&=&28-20 \\ &&&&y&=&8 \\ (-4,8)&&&&&& \end{array}
  20. \begin{array}{rrrrrrrll} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ &&(-x&-&4y&=&-14)&(-1)& \\ &&x&+&4y&=&14&& \\ &&&-&4y&&-4y&& \\ \midrule &&&&x&=&14&-&4y \\ \\ &&(-6x&+&8y&=&12)&\div &2 \\ &&-3x&+&4y&=&6&& \\ -3(14&-&4y)&+&4y&=&6&& \\ -42&+&12y&+&4y&=&6&& \\ +42&&&&&&+42&& \\ \midrule &&&&\dfrac{16y}{16}&=&\dfrac{48}{16}&& \\ \\ &&&&y&=&3&& \\ \\ &&&&x&=&14&-&4(3) \\ &&&&x&=&14&-&12 \\ &&&&x&=&2&& \\ (2,3)&&&&&&&& \end{array}

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