Linear Equation Solver — 2 Variables
Enter coefficients for ax+by=c and dx+ey=f to calculate the unique intersection when one exists.
Solve a·x + b·y = c and d·x + e·y = f.
Determinant-3
x2.666667
y1.666667
How this tool works
Cramer’s rule uses determinant Δ=ae−bd, with x=(ce−bf)/Δ and y=(af−cd)/Δ when Δ≠0.
Example
The equations 2x+y=7 and x−y=1 solve to x=8/3 and y=5/3.
Common questions
What if the determinant is zero?
The equations do not have a unique solution; they may be parallel/inconsistent or represent the same line.
Can this solve nonlinear equations?
No. It is specifically for two linear equations in two unknowns.