AlgebraFoundation and Higher

Simultaneous equations: GCSE maths practice with worked answers

Show Working has 1 kind of simultaneous equations question for GCSE Maths, for Foundation and Higher. Every question is new each time and comes with the working, step by step.

Simultaneous equations are two equations with two unknowns that are true at the same time. Show Working uses elimination: add or subtract the equations to remove one letter, solve for the other, then substitute back.

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Worked example 1: simultaneous equations (elimination)

Solve these simultaneous equations.
3x + 2y = −26
x − 2y = 2

Call the equations (1) and (2). The y terms are 2y and −2y, so we can eliminate y.
The y terms have opposite signs, so ADD the equations: 4x = −24.
Divide by 4: x = −24 ÷ 4 = −6.
Put x = −6 into equation (1): 3 × (−6) + 2y = −26, so 2y = −8.
Divide by 2: y = −4.
Check in equation (2): 1 × (−6) − 2 × (−4) = 2. It works.

Answer x = −6, y = −4

01 / What's covered1 kind of question

Simultaneous equations questions in the app

Each kind makes fresh questions every time, so you can practise as often as you like.

Simultaneous equations (elimination)Both tiers

Worked example 2: simultaneous equations (elimination)

Solve these simultaneous equations.
6x + y = −12
x − y = −9

Call the equations (1) and (2). The y terms are y and −y, so we can eliminate y.
The y terms have opposite signs, so ADD the equations: 7x = −21.
Divide by 7: x = −21 ÷ 7 = −3.
Put x = −3 into equation (1): 6 × (−3) + y = −12, so y = 6.
Check in equation (2): 1 × (−3) − 1 × 6 = −9. It works.

Answer x = −3, y = 6

A common mistake

Forgetting to find the second value. Once you have x, put it back into one of the equations to find y, and check both.

02 / Practise itiPhone and iPad

Practise simultaneous equations in Show Working

In the app, open Topics and choose Simultaneous equations for ten fresh questions. Ask for a hint if you are stuck, and open the working to see the method one step at a time.