Math

Elimination Method Calculator

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

a₁

b₁

c₁

a₂

b₂

c₂

Calculated Output

x 3

y 1.5

Formula: Scale equations so one variable cancels when added

Step-by-Step Breakdown

1. Values used:

2. a₁ = 3

3. b₁ = 2

4. c₁ = 12

5. a₂ = 1

6. b₂ = -2

7. c₂ = 0

9. x = 3

10. y = a₁ / b₁ = 3 / 2 = 1.5

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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.

Frequently Asked Questions

Elimination vs substitution?

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

The math behind it

Worked Example

Frequently Asked Questions

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