Read the result
The determinant tells you whether the two equations have one crossing point. If it vanishes, the graph decides whether the lines are parallel or coincident.
Linear systems
2x2 Linear System Solver
Solve two linear equations and see whether the lines meet once, never meet, or are really the same line.
Formula
Delta = a1*b2 - a2*b1; x = (c1*b2 - c2*b1)/Delta; y = (a1*c2 - a2*c1)/Delta
Result
Worked substitution
Each equation is a line. A unique solution is the point where the two lines meet.
Where it helps
Use this for quick simultaneous-equation checks before moving to matrix methods.
Common slip
A zero determinant does not automatically mean no solution. Coincident lines give infinitely many solutions.
Try it
Change the second equation to be twice the first. The solver should move from one solution to infinitely many.