System of Equations Calculator

Solve two simultaneous linear equations for x and y.

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Enter your values below.

Result

x =

y =

Solves a₁x + b₁y = c₁ and a₂x + b₂y = c₂ using Cramer's rule (determinants).

Example: x + y = 10 and 2x − y = 5 → x = 5, y = 5.

Enter a₁ (eq. 1, coeff. of x), b₁ (eq. 1, coeff. of y), c₁ (eq. 1, result), a₂ (eq. 2, coeff. of x), b₂ (eq. 2, coeff. of y), c₂ (eq. 2, result).
Press Calculate to see your result instantly.

FAQ

What method is used to solve the system?

Cramer's rule, which uses determinants to solve for x and y directly.

What if there's no unique solution?

If the two equations are parallel (or identical), the calculator shows an error since there's no single solution.

Can I solve three or more equations?

This tool handles exactly two equations with two unknowns.

What do the coefficients represent?

Each equation is in the form (coefficient of x) × x + (coefficient of y) × y = (result).