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Elimination Method Calculator

This calculator solves systems of linear equations using the elimination method. It eliminates one variable by adding or subtracting equations, allowing you to find the solution step by step. Ideal for algebra students and anyone solving two-variable systems.

Solve Linear Systems with the Elimination Method

Input Fields
a₁
b₁
c₁
a₂
b₂
c₂
If enabled, the result will update automatically when you change any value.

Elimination Method for Solving Systems of Equations

Formula
$$\begin{aligned} a_1x + b_1y &= c_1 \\ a_2x + b_2y &= c_2 \end{aligned}$$

Multiply one or both equations so the coefficients of $$x$$ or $$y$$ are equal (or opposites), then add or subtract the equations to eliminate a variable and solve.

Elimination Method – Calculation Example

System:
2x + 3y = 16
4x – 3y = 4

Step 1: Add both equations →
(2x + 3y) + (4x – 3y) = 16 + 4
→ 6x = 20 → x = 20 / 6 = 10 / 3

Step 2: Substitute x into one equation:
2(10/3) + 3y = 16
20/3 + 3y = 16
3y = 16 – 20/3 = (48 – 20)/3 = 28/3
y = 28 / 9

Result:
x = 10/3, y = 28/9

The elimination method is a systematic approach to solving linear equations, especially when substitution is inefficient. It’s a core technique in algebra courses and is foundational in linear algebra and systems modeling. This calculator handles fractional and integer coefficients, showing detailed steps.

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