📐 System of Linear Equations Calculator
Solve a system of two linear equations with two unknowns (x and y) using Cramer’s rule.
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What this calculator solves
This calculator finds the values of x and y that satisfy two linear equations at the same time, written as a1x + b1y = c1 and a2x + b2y = c2. Geometrically, this is the point where two straight lines intersect.
The formula used
The solution is found using Cramer’s rule. The main determinant is D = a1·b2 – b1·a2. Then x = (c1·b2 – b1·c2) / D and y = (a1·c2 – c1·a2) / D. If D equals zero, the two lines are parallel (or identical) and there is no single unique solution.
This tool is intended for general math and engineering learning purposes.
Last reviewed August 2026