Systems of Equations: Substitution vs Elimination
Solve a system of two linear equations by substitution or elimination, and learn which method to choose, with two worked examples.
Pick your method
- Substitution: one variable already alone (y = …)
- Elimination: both equations in the form Ax + By = C
Either method gives the same answer.
The steps
- Get one variable by itself, or line up like terms
- Combine or substitute to remove one variable
- Solve, then plug back in and check
Always check in both equations.
Example 1: elimination
Solve 2x + y = 7 and x − y = 2.
- Add the equations: the y terms cancel
- 3x = 9, so x = 3
- Plug in: 3 − y = 2, so y = 1
(x, y) = (3, 1)
Example 2: substitution
Solve y = 2x − 1 and 3x + y = 9.
- Substitute: 3x + (2x − 1) = 9
- 5x = 10, so x = 2
- y = 2(2) − 1
(x, y) = (2, 3)
Common mistake
Subtracting a negative term without changing the sign
When you subtract an equation, change every sign in it.
If no variable cancels, multiply one equation first.
A false statement like 0 = 5 means no solution.
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