Mathematics & Statistics / Algebra
Simultaneous Equations Solver
Equation 1: a₁x + b₁y = c₁
Equation 2: a₂x + b₂y = c₂
Method
Uses Cramer's rule to solve the system of linear equations.
Solve systems of equations quickly to find consistent variable values for algebra, analytics, and applied math scenarios.
Formula
For linear systems Ax = b, solution is x = A^(-1)b when A is invertible; elimination/substitution methods also apply.
Worked Example
equation12x + y = 11
equation2x - y = 1
Result: x = 4, y = 3The two linear equations intersect at a single point, giving one unique solution pair for both variables.
Frequently Asked Questions
What if there is no solution?
Parallel but distinct lines produce no common intersection, so the system is inconsistent.
Can systems have infinitely many solutions?
Yes. If equations are dependent representations of the same line, every point on that line is a solution.