Math Calculators

Cramer's Rule Calculator (2×2 System)

Solve a system of two linear equations using Cramer's rule, showing every determinant involved.

D (main determinant) —

Dₓ —

D_y —

x —

y —

About the Cramer's Rule Calculator (2×2 System)

Cramer's rule solves a system of linear equations using ratios of determinants, replacing one column of the coefficient matrix at a time with the constants.

Formula: Given a₁x + b₁y = c₁ and a₂x + b₂y = c₂: D = a₁b₂ − a₂b₁, D_x = c₁b₂ − c₂b₁, D_y = a₁c₂ − a₂c₁, then x = D_x/D and y = D_y/D

If D = 0, the system has no unique solution. Cramer's rule is a direct, elegant alternative to elimination or substitution for small systems.