Edexcel International GCSE Mathematics A · 4MA1
Simultaneous equations
Simultaneous solutions satisfy both equations at the same time. Elimination removes one variable by adding or subtracting matched equations. Substitution is useful when an equation already gives one variable in terms of the other.
Key method
Multiply every term of an equation by the same number before eliminating. Substitute the first solution back to recover the other variable.
Worked example
Solve 2x + y = 11 and x − y = 1.
- Add the equations: 3x = 12 because y + (−y) = 0.
- Divide by 3 to get x = 4.
- Substitute into x − y = 1: 4 − y = 1, so y = 3.
Answer and interpretation
x = 4, y = 3; both original equations are satisfied.
Common mistake
Subtracting equations without brackets can change only one sign instead of all signs.
Practise independently
Solve 3x + y = 14 and x + y = 6.
Check your answer
Subtract: 2x = 8. Hence x = 4 and y = 2.
Syllabus connection
This lesson develops simultaneous linear equations within the algebra area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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