System of Equations Calculator
Solve two linear equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂.
Solve a 2×2 system of linear equations using Cramer's rule.
The math behind it
The determinant D = a₁b₂ − b₁a₂. If D ≠ 0 there is one solution: x = (c₁b₂ − b₁c₂)/D and y = (a₁c₂ − c₁a₂)/D. If D = 0 the lines are parallel or identical.
Worked example
2x + 3y = 6 and x − y = −2 → x = 0, y = 2.
FAQ
What does a zero determinant mean?
No unique solution: the equations are either inconsistent (no solution) or dependent (infinitely many).