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
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.
Solve x + y = 10 and x − y = 2
Solve 3x + y = 11 and x + y = 5
Solve 2x + 3y = 16 and x + y = 6
Solve 5x − 2y = 4 and 3x + 2y = 12
The sum of two numbers is 18 and their difference is 4. Find the numbers.
Common mistakes
- Adding when you should subtract (or the reverse) after lining up coefficients.
- Only multiplying one side of an equation.
- Finding x and forgetting to find y.
Answers and working
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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