How to Use the Simultaneous Equations Solver
The Simultaneous Equations Solver finds solutions for systems of 2 or 3 linear equations. Enter the coefficients for each variable and the right-hand side constant, and the solver returns the value of x, y, and (for 3-variable systems) z. It uses Cramer's rule for 2-variable systems and Gaussian elimination with partial pivoting for 3-variable systems.
If the determinant is zero or near zero, the system has no unique solution — either no solution or infinitely many — and an error is shown. Decimal coefficients are fully supported.
Methods Used
2 variables: x = (c₁b₂−b₁c₂)/det, y = (a₁c₂−c₁a₂)/det, where det = a₁b₂−b₁a₂. 3 variables: forward elimination with row swapping to maximize pivot size, followed by back substitution.
Frequently Asked Questions
No. The mathematical result is the same regardless of which equation you enter first.
Yes. Enter 0 for any coefficient that is absent. For example, 2x + 0y = 6 means b = 0.
No. This solver is for linear equations only. Nonlinear terms are not supported.