2x2 Cramers Rule Calculator

About this calculator

Cramer's rule, named after the Swiss mathematician Gabriel Cramer, solves a system of linear equations using determinants instead of substitution or elimination. For a 2×2 system (two equations, two unknowns x and y), you first compute the determinant D of the coefficient matrix, then form two more matrices by replacing one column at a time with the constants from the right-hand side of the equations, giving determinants Dx and Dy; the solution is simply x = Dx/D and y = Dy/D, provided D is not zero.

Cramer's rule is taught widely in algebra and linear algebra courses as a clean, formulaic alternative to elimination, and it's used in engineering, physics and economics whenever a small system of linear equations, such as balancing forces, currents in a circuit, or supply-and-demand equations, needs a quick, direct solution without row-reducing a matrix by hand.

Enter the coefficients of your two linear equations and this calculator finds x, y and the determinant using Cramer's rule.