Two equations, two unknowns calculator

How it works

Enter the coefficients of two linear equations ax + by = c to find x and y.

The formula

Cramer's rule: D = a₁b₂ − a₂b₁, x = (c₁b₂ − c₂b₁) ÷ D, y = (a₁c₂ − a₂c₁) ÷ D.

Worked example

2x + y = 7 and x − y = 2: D = −2 − 1 = −3, x = (−7 − 2) ÷ −3 = 3, y = (4 − 7) ÷ −3 = 1.

Good to know

• If D = 0 the lines are parallel (no solution) or the same line (infinitely many).