Year 10 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.

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.The sum of two numbers is 25 and their difference is 7. What is the larger number?
2.How many solutions does the pair x + 2y = 4 and 2x + 4y = 12 have?
- a) Exactly one
- b) None
- c) Exactly two
- d) Infinitely many
3.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.
4.Solve the pair 3x + 2y = 12 and x = 2. What is y?
5.For which of these pairs do the two lines cross at exactly one point?
- a) x + y = 5 and x + y = 8
- b) 2x + 3y = 6 and 4x + 6y = 5
- c) x + 2y = 5 and 2x + y = 4
- d) x + y = 5 and 2x + 2y = 10
6.Solve the pair x + y = 10 and x - y = 4. What is y?
7.Sort each pair of equations by whether its two lines ever meet.
Groups: They meet · They never meet
- 2x + y = 7 and x + 3y = 6
- 2x - y = 1 and x + 2y = 8
- x + y = 4 and 2x + 2y = 9
- 3x + 2y = 6 and 6x + 4y = 5
- x + y = 4 and x - y = 2
- x + 5y = 2 and 2x + 10y = 9
8.The sum of two numbers is 25 and their difference is 7. What is the smaller number?

Answer key — Year 10 Maths — Pair of linear equations

1. 16
2. b) None
3. 400
4. 3
5. c) x + 2y = 5 and 2x + y = 4
6. 3
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. 9