Quick answer: In substitution, express one variable using the other, then replace that variable in the second equation. A solution must satisfy both equations.
Worked example
Solve x + y = 9 and 2x − y = 3.
- From the first equation, y = 9 − x.
- Substitute into the second: 2x − (9 − x) = 3.
- Simplify: 3x − 9 = 3, so x = 4.
- Then y = 9 − 4 = 5.
Check the result
4 + 5 = 9 and 2(4) − 5 = 3.
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Common mistake to avoid
Keep brackets around the substituted expression, especially after a minus sign. Finding x alone does not complete a pair of equations.
Try it yourself
1. Solve y = 2x and x + y = 12. 2. Solve x − y = 2 and x + y = 10.
Answers and reasoning
1. 3x = 12 gives x = 4, y = 8. 2. x = y + 2 gives 2y + 2 = 10, so y = 4, x = 6.
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