System of Equations Solver
Solve linear systems up to 6x6 with Gaussian elimination steps, Cramer's rule and exact fractions, plus nonlinear systems shown on a graph.
Graph
Drag to pan, scroll or pinch to zoom, hover or tap a curve to trace it, click a gray point to pin its coordinates.
Step-by-step solution
About System of Equations Solver
The system of equations solver handles linear systems from 2 to 6 unknowns, typed as equations or entered as a coefficient grid. Fractions and decimals are kept exact, so the solution comes out as clean fractions with no rounding.
Gaussian elimination (Gauss-Jordan) is shown row operation by row operation with the augmented matrix after each step, and Cramer's rule is available for square systems with a non-zero determinant. The matrix form A x = b is displayed too.
The solver tells you whether there is one solution, none, or infinitely many, and writes the general solution with parameters. Two nonlinear equations in x and y are solved numerically and shown as curve intersections on the graph.
How to use System of Equations Solver
- Type one equation per line, such as 2x + 3y = 8, or switch to the coefficient grid.
- Choose Gaussian elimination or Cramer's rule.
- Read the solution and its type: one solution, no solution or infinitely many.
- Open the steps to follow each row operation or each determinant.
- For two unknowns, look at the graph to see the lines or curves meet.