Foundation (simple) & Higher

Simultaneous equations: GCSE Maths revision

Simultaneous equations are two equations with two unknowns. You need a pair of values that works in both. Use elimination or substitution.

Elimination

Solve 2x + y = 11 and x + y = 7

Subtract: (2x + y) − (x + y) = 11 − 7 → x = 4
Substitute into x + y = 7 → 4 + y = 7 → y = 3
Check in the first equation: 2(4) + 3 = 11 ✓

When coefficients do not match

Multiply one or both equations so that the x or y coefficients match (or are equal and opposite), then add or subtract.

Try these questions

Cover the answers and have a go first. Worked solutions are underneath.

Question 1 [2 marks]

Solve x + y = 10 and x − y = 2

Question 2 [2 marks]

Solve 3x + y = 11 and x + y = 5

Question 3 [3 marks]

Solve 2x + 3y = 16 and x + y = 6

Question 4 [3 marks]

Solve 5x − 2y = 4 and 3x + 2y = 12

Question 5 [3 marks]

The sum of two numbers is 18 and their difference is 4. Find the numbers.

Common mistakes

Answers and working

Q1. x = 6, y = 4
Q2. x = 3, y = 2
Q3. x = 2, y = 4
Q4. x = 2, y = 3
Q5. 11 and 7

Frequently asked questions

Elimination or substitution?

Elimination is fast when coefficients already match. Substitution is useful when one equation is already x = … or y = ….

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