GCSE · Simultaneous equations

Simultaneous equations by eliminationExam-style questions

Why two unknowns need two equations, why adding or subtracting whole equations is legal, and the sign rule that decides which of the two kills a variable.

Start practising Read the lesson

18 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Solve the simultaneous equations

$5x + 2y = 11$ $3x + 5y = 18$
Level 4 · 4 marksTry it
2
Solve the simultaneous equations

$2x - 3y = 13$ $3x + 2y = 13$
Level 4 · 4 marksTry it
3
A cinema sells adult tickets and child tickets.

3 adult tickets and 2 child tickets cost £24.30.

2 adult tickets and 3 child tickets cost £21.20.

Work out the cost of one adult ticket and the cost of one child ticket.
Level 4 · 4 marksTry it
4
Solve the simultaneous equations

$2x + 5y = 24$ $x + 2y = 10$
Level 4 · 3 marksTry it
5
Solve the simultaneous equations

$3x + 2y = 12$ $5x + 3y = 19$
Level 4 · 3 marksTry it