System of Equations Solver
Solve 2×2 and 3×3 simultaneous equations step-by-step using substitution, elimination, and Cramer's determinant rule.
Awaiting Input
Enter any equation like 2x + 8 = 20 or x² - 5x + 6 = 0 to get step-by-step solutions.
Methods for Solving Systems
A system of linear equations consists of two or more equations with shared variables. The solution is the point (x, y) where all lines intersect.
Frequently Asked Questions
How does the system of equations solver work?
Enter your equations separated by commas (e.g. 2x + y = 7, x - y = 2). The solver sets up the matrix form Ax = b and computes the determinant using Cramer's Rule or Gaussian elimination to find the exact intersection point.
Can it solve 3-variable systems?
Yes, it supports systems with x, y, and z variables using row reduction and back-substitution.
What happens if a system has no solution?
When the determinant is zero, the solver identifies whether the lines are parallel (inconsistent / no solution) or coincident (infinitely many solutions).