System Of Equations Calculator

Use this free system of equations calculator to solve a system of two linear equations for x and y.

How the system of equations calculator works

For a₁x + b₁y = c₁ and a₂x + b₂y = c₂, Cramer’s rule gives x = (c₁b₂ − c₂b₁) ÷ D and y = (a₁c₂ − a₂c₁) ÷ D, where D = a₁b₂ − a₂b₁.

Frequently asked questions

What if the determinant is zero?

Then the lines are parallel (no solution) or the same line (infinitely many solutions).

Results are estimates for general information only. They are not a substitute for professional advice where applicable. Found a mistake? Report an error.