Solve a system of two linear equations in two unknowns using Cramer's rule.
Cramer's rule solves a 2×2 system by computing the determinant of the coefficient matrix and substituting columns with the constants vector. If det = 0, the lines are parallel (no solution) or coincident (infinite solutions).
Determinant
det = a₁·b₂ − a₂·b₁
Solution
x = (c₁·b₂ − c₂·b₁) / det, y = (a₁·c₂ − a₂·c₁) / det
The two lines are either parallel (no solution) or identical (infinitely many solutions). This calculator reports an error in that case.
This calculator handles 2×2 systems. For larger systems, use the matrix calculator or Gaussian elimination.