Answer Key 5.1

  1. (-1,2)
    lines intersect at -1, 2
  2. (-4,3)
    lines intersect at -4, 3
  3. (-1,-3)
    lines intersect at -1, -3
  4. (-3,1)
    lines intersect at -3, 1
  5. Parallel lines ∴ no intersection
    graph showing parallel lines therefore no intersection
  6. (-2,-2)
    lines intersect at -2, -2
  7. (-3,1)
    -3, 1
  8. (1,-2)
    lines intersect at 1,-2
  9. (-3,-1)
    lines intersect -3,-1
  10. Parallel lines ∴ no intersection
    graph showing parallel lines therefore no intersection
  11. \begin{array}{rrrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ x&+&3y&=&-9\hspace{0.25in}&5x&+&3y&=&3 \\ -x&&&&-x\hspace{0.25in}&-5x&&&&-5x \\ \midrule \dfrac{3y}{3}&=&\dfrac{-x}{3}&-&\dfrac{9}{3}\hspace{0.25in}&\dfrac{3y}{3}&=&\dfrac{-5x}{3}&+&\dfrac{3}{3} \\ \\ y&=&-\dfrac{1}{3}x&-&3\hspace{0.25in}&y&=&-\dfrac{5}{3}x&+&1 \\ \\ (3,-4)&&&&&&&&& \end{array}
    3,-4
  12. \begin{array}{rrrrrrrrrr} \\ \\ \\ \\ \\ \\ \\ x&+&4y&=&-12\hspace{0.25in}&2x&+&y&=&4 \\ -x&&&&-x\hspace{0.25in}&-2x&&&&-2x \\ \midrule \dfrac{4y}{4}&=&\dfrac{-x}{4}&-&\dfrac{12}{4} \hspace{0.25in}&y&=&-2x&+&4 \\ \\ y&=&-\dfrac{1}{4}x&+&3 \hspace{0.25in}&y&=&-2x&+&4 \\ \\ (4,-4)&&&&&&&&& \end{array}
    lines intersect at 4,-4

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Intermediate Algebra by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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