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Homework: Simultaneous Equations

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

Summary: Some homework problems on simultaneous equations.

Exercise 1

Years after their famous race, the tortoise and the hare agree on a re-match. As they begin the race, the tortoise plods along at 2 1 2 2 1 2 mph, slow but confident. The hare zips out at 8 1 2 8 1 2 mph, determined not to repeat his original mistake... and he doesn't! The hare never slows down, and reaches the finish line 45 minutes (that is, 3 4 3 4 of an hour) before the tortoise.

  • a. Did they run the same amount of time as each other?
  • b. Did hey run the same distance?
  • c. Clearly define and label the two variables in this problem. Note that your answers to (a) and (b) will have a lot to do with how you do this?
  • d. Based on your variables, write the equation d = r t d=rt for the tortoise.
  • e. Based on your variables, write the equation d = r t d=rt for the hare.
  • f. Now answer the question: how long did the tortoise run?

Exercise 2

6x + 2y = 6 6x + 2y = 6 size 12{6x+2y=6} {}

x y = 5 x y = 5 size 12{x - y=5} {}

  • a. Solve by substitution.
  • b. Check your answers.

Exercise 3

3x + 2y = 26 3x + 2y = 26 size 12{3x+2y="26"} {}

2x 4y = 4 2x 4y = 4 size 12{2x - 4y=4} {}

  • a. Solve by substitution.
  • b. Check your answers.

Exercise 4

2y x = 4 2y x = 4 size 12{2y - x=4} {}

2x + 20 y = 4 2x + 20 y = 4 size 12{2x+"20"y=4} {}

  • a. Solve by substitution.
  • b. Check your answers.

Exercise 5

7 x - 3 = y 7x-3=y

14 x = 2 y + 6 14x=2y+6

  • a. Solve by substitution.
  • b. Check your answers.

Exercise 6

3x + 4y = 12 3x + 4y = 12 size 12{3x+4y="12"} {}

5x 3y = 20 5x 3y = 20 size 12{5x - 3y="20"} {}

  • a. Solve any way you like.
  • b. Check your answers.

Exercise 7

ax + y = 6 ax + y = 6 size 12{ ital "ax"+y=6} {}

2x + y = 4 2x + y = 4 size 12{2x+y=4} {}

  • a. Solve any way you like. You are solving for xx size 12{x} {} and yy size 12{y} {}; aa size 12{a} {} is just a constant. (So your final answer will say “ xx size 12{x} {}=blah-blah, yy size 12{y} {}=blah-blah.” The blah-blah will both have aa size 12{a} {} in them.)
  • b. Check your answers.

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