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Grade 8 Math — Pair of linear equations

Solve a pair of linear equations in two variables by substitution and elimination, and say how many solutions a pair has.

Name: ________________________

Before you start

One scale, and every box on it hides the same weight. Move things about and find out what a single scale can and cannot tell you.

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A scale can pin down one unknown, never two at once — which is exactly why a pair of equations is needed. Elimination is the step that turns the pair into a single scale like this one.

  1. 1.Two adult tickets and one child ticket cost 900 $. One adult ticket and one child ticket cost 500 $. What does one child ticket cost? Give just the number.

  2. 2.Solve the pair 5x - 2y = 16 and x + 2y = 8. What is x?

  3. 3.For which of these pairs do the two lines cross at exactly one point?

    • a) x + 2y = 5 and 2x + y = 4
    • b) x + y = 5 and 2x + 2y = 10
    • c) 2x + 3y = 6 and 4x + 6y = 5
    • d) x + y = 5 and x + y = 8

  4. 4.Two adult tickets and one child ticket cost 900 $. One adult ticket and one child ticket cost 500 $. What does one adult ticket cost? Give just the number.

  5. 5.Match each pair of equations to the value of x that solves it.

    • x + y = 6 and x - y = 2
    • x + y = 9 and x - y = 1
    • x + y = 12 and x - y = 4
    • x + y = 14 and x - y = 8
    • 4
    • 8
    • 11
    • 5

  6. 6.The sum of two numbers is 25 and their difference is 7. What is the smaller number?

  7. 7.Solve the pair 2x + y = 11 and x - y = 1. What is x?

  8. 8.Solve the pair x + y = 10 and x - y = 4. What is y?

Answer key — Grade 8 Math — Pair of linear equations

  1. 1. 100
  2. 2. 4
  3. 3. a) x + 2y = 5 and 2x + y = 4
  4. 4. 400
  5. 5. x + y = 6 and x - y = 2 → 4; x + y = 9 and x - y = 1 → 5; x + y = 12 and x - y = 4 → 8; x + y = 14 and x - y = 8 → 11
  6. 6. 9
  7. 7. 4
  8. 8. 3