Cramer's Rule Calculator (2×2)
The Cramer's Rule Calculator solves a 2×2 system of linear equations using determinants. Enter the coefficients and constants for a₁₁x + a₁₂y = b₁ and a₂₁x + a₂₂y = b₂.
Formula
x = det(Aₓ) ÷ det(A), y = det(A_y) ÷ det(A)
- Aₓ replaces the x-column with the constants; A_y replaces the y-column.
- A zero coefficient determinant means the system has no unique solution.
2x + y = 5, x + 3y = 10
Inputs
- a₁₁: 2
- a₁₂: 1
- b₁: 5
- a₂₁: 1
- a₂₂: 3
- b₂: 10
det = 5, x = (5·3 − 1·10)/5 = 1, y = (2·10 − 5·1)/5 = 3.
Frequently asked questions
When can't you use Cramer's rule?
When the coefficient determinant is zero, the system has either no solution or infinitely many.