GCSE algebra
Simultaneous equations: elimination method
Use this guide as a revision starting point, then practise with questions matched to your course and exam board.
Simultaneous equations contain two unknown values that must satisfy both equations. Elimination works by making one variable disappear when the equations are added or subtracted.
Worked example
2x + y = 11
3x − y = 9Add the equations: 5x = 20, so x = 4. Substitute into the first equation: 2(4) + y = 11, so y = 3.
Checks
- Substitute both values into both original equations.
- Write one operation per line.
- When signs are the same, subtract; when signs are opposite, add.