GCSE MATHS PRACTICE
GCSE Simultaneous Equations Questions
Linear simultaneous equations have two unknowns and must be satisfied by the same pair of values. In elimination, match the coefficient of one unknown, multiplying an entire equation if needed, then add or subtract to remove that unknown. Substitute back to find the other value and check both original equations.
Updated 8 October 2026
Worked example
Solve 3x + 2y = 23 and x + 2y = 13.
- Subtract the second equation from the first: (3x + 2y) − (x + 2y) = 23 − 13, so 2x = 10.
- Divide by 2: x = 5. Substitute into x + 2y = 13 to obtain 5 + 2y = 13, so y = 4.
- Check both equations: 3 × 5 + 2 × 4 = 23 and 5 + 2 × 4 = 13.
Answer: x = 5, y = 4
Practice questions
- 1
Solve x + y = 11 and x − y = 3.
- 2
Solve 2x + y = 17 and x − y = 4.
- 3
Solve 3x + 2y = 25 and 2x + 3y = 20.
- 4
Two notebooks and one pen cost £9. Three notebooks and two pens cost £14. Find the price of one notebook and one pen.
Show answers
- 1. x = 7, y = 4
- 2. x = 7, y = 3
- 3. x = 7, y = 2
- 4. Notebook £4; pen £1
Common mistakes
- Multiplying only one term — Multiply every term and the right-hand side when scaling an equation.
- Subtracting signs incorrectly — Subtract the whole equation, including any negative terms.
- Stopping after one unknown — Find both values and check the pair in both original equations.