Elimination Method Calculator

Solve a 2×2 linear system by elimination (addition).

x 3
y 1.5

Formula: Scale equations so one variable cancels when added

Step-by-step with your numbers:
1. Values used:
2. a₁ = 3
3. b₁ = 2
4. c₁ = 12
5. a₂ = 1
6. b₂ = -2
7. c₂ = 0
8.
9. x = 3
10. y = a₁ / b₁ = 3 / 2 = 1.5
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The elimination method multiplies the equations so that adding them removes one variable.

The math behind it

Multiply each equation by a constant so the coefficients of one variable are opposite, then add to eliminate it. Solve for the remaining variable and back-substitute.

Worked example

3x + 2y = 12 and x − 2y = 0 → add: 4x = 12, x = 3, y = 1.5.

FAQ

Elimination vs substitution?

Both give the same answer; elimination is handy when coefficients line up for easy cancellation.