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Homework: Simultaneous Equations by Graphing

Module by: Kenny M. Felder. E-mail the author

Summary: Some homework problems on solving simultaneous equations by graphing.

In each problem, find all x x size 12{x} {} and y y size 12{y} {} values that satisfy both conditions. Your answers may be approximate.

Exercise 1

2y=6x+102y=6x+10 size 12{2y=6x+"10"} {} and 3y=12x+93y=12x+9 size 12{3y="12"x+9} {}

  • a. Put both equations into y=mx+by=mx+b size 12{y= ital "mx"+b} {} format. Then graph them.
  • b. List all points of intersection.
  • c. Check these points to make sure they satisfy both equations.

Exercise 2

y = 2x 3 y = 2x 3 size 12{y=2x - 3} {} and 3y = 6x + 3 3y = 6x + 3 size 12{3y=6x+3} {}

  • a. Put both equations into y=mx+by=mx+b size 12{y= ital "mx"+b} {} format. Then graph them.
  • b. List all points of intersection.
  • c. Check these points to make sure they satisfy both equations.

Exercise 3

y=x3y=x3 size 12{y=x - 3} {} and 2y=2x62y=2x6 size 12{2y=2x - 6} {}

  • a. Put both equations into y=mx+by=mx+b size 12{y= ital "mx"+b} {} format. Then graph them.
  • b. List all points of intersection.
  • c. Check these points to make sure they satisfy both equations.

Exercise 4

y = x y = x size 12{y=x} {} and y = x 2 1 y = x 2 1 size 12{y=x rSup { size 8{2} } - 1} {}

  • a. Graph them both on the back.
  • b. List all points of intersection.
  • c. Check these points to make sure they satisfy both equations.

Exercise 5

y = x 2 + 2 y = x 2 + 2 size 12{y=x rSup { size 8{2} } +2} {} and y = x y = x size 12{y=x} {}

  • a. Graph them both on the back.
  • b. List all points of intersection.
  • c. Check these points to make sure they satisfy both equations.

Exercise 6

y = x 2 + 4 y = x 2 + 4 size 12{y=x rSup { size 8{2} } +4} {} and y = 2x + 3 y = 2x + 3 size 12{y=2x+3} {}

  • a. Put the second equation into y=mx+by=mx+b size 12{y= ital "mx"+b} {} format. Then graph them both on the back.
  • b. List all points of intersection.
  • c. Check these points to make sure they satisfy both equations.

Exercise 7

Time for some generalizations…

  • a. When graphing two lines, is it possible for them to never meet? _______
  • To meet exactly once? _________
  • To meet exactly twice? _________
  • To meet more than twice? ___________
  • b. When graphing a line and a parabola, is it possible for them to never meet? _______
  • To meet exactly once? _________
  • To meet exactly twice? _________
  • To meet more than twice? ___________

This last problem does not involve two lines, or a line and a parabola: it’s a bit weirder than that. It is the only problem on this sheet that should require a calculator.

Exercise 8

y = 6x x 2 + 1 y = 6x x 2 + 1 size 12{y= { {6x} over {x rSup { size 8{2} } +1} } } {} and y = 4 x 5 y = 4 x 5 size 12{y=4 sqrt {x} - 5} {}

  • a. Graph them both on your calculator and find the point of intersection as accurately as you can.
  • b. Check this point to make sure it satisfies both equations.

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