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Year 11 Maths — 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.

113

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 3x + 2y = 12 and x = 2. What is y?

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

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

  5. 5.How many solutions does the pair x + 2y = 4 and 2x + 4y = 12 have?

    • a) None
    • b) Infinitely many
    • c) Exactly one
    • d) Exactly two

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

  7. 7.Sort each pair of equations by whether its two lines ever meet.

    Groups: They meet · They never meet

    • 3x + 2y = 6 and 6x + 4y = 5
    • x + y = 4 and 2x + 2y = 9
    • 2x - y = 1 and x + 2y = 8
    • x + y = 4 and x - y = 2
    • 2x + y = 7 and x + 3y = 6
    • x + 5y = 2 and 2x + 10y = 9

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

Answer key — Year 11 Maths — Pair of linear equations

  1. 1. 100
  2. 2. 3
  3. 3. 7
  4. 4. 4
  5. 5. a) None
  6. 6. 4
  7. 7. x + y = 4 and x - y = 2 → They meet; x + y = 4 and 2x + 2y = 9 → They never meet; 2x + y = 7 and x + 3y = 6 → They meet; 3x + 2y = 6 and 6x + 4y = 5 → They never meet; 2x - y = 1 and x + 2y = 8 → They meet; x + 5y = 2 and 2x + 10y = 9 → They never meet
  8. 8. 3