Solve a system of two linear equations for x and y — free and instant.
Enter the coefficients of two linear equations in the standard form a₁x + b₁y = c₁ and a₂x + b₂y = c₂, and this solves for x and y using Cramer's rule.
Three outcomes are possible, and this tool distinguishes between them rather than just reporting numbers: a unique solution (the two lines cross at exactly one point), no solution (the lines are parallel and never meet), or infinitely many solutions (the two equations describe the same line).
The two lines are parallel — same slope, different intercepts — so they never cross.
Both equations describe the exact same line, just written differently (for example, one might be a multiple of the other) — every point on that line satisfies both equations.
Cramer's rule — computing three determinants and dividing, which is equivalent to elimination or substitution but avoids multi-step algebra.