Linear Equation Solver
Solve systems of two linear equations with two unknowns. Find x and y values instantly.
How to Use This Calculator
Enter your values in the fields above and click "Calculate" to get instant results. This linear equation solver provides accurate results with step-by-step explanations.
Formula
x = (c₁b₂ - c₂b₁) / (a₁b₂ - a₂b₁)
Quick Examples
- 2x+3y=8, x-y=-1 → x=1, y=2
- 3x+2y=12, x+y=5 → x=2, y=3
Frequently Asked Questions
How does Cramer's rule work?
Cramer's rule uses determinants to solve systems of linear equations. For 2 variables: x = (c₁b₂-c₂b₁)/(a₁b₂-a₂b₁).
What if the determinant is zero?
If the determinant is zero, the system either has no solution (parallel lines) or infinitely many solutions (same line).