System of Linear Equations Solver

Solve systems of linear equations (2×2, 3×3, n×n) with Gaussian elimination. Detects unique, infinite or no solutions.

Results

Solution—
Rank of A—

How to use the System of Linear Equations Solver

  1. Enter or select: Augmented matrix [A | b], one equation per line.
  2. The results (Solution, Rank of A) are calculated instantly as you type.
  3. Use “Copy link” to share the calculation with the same input values.

Formula

  • A·x = b
  • Gauss–Jordan elimination with partial pivoting

About this tool

Write each equation as a row of numbers. For example 2x + y − z = 8 becomes 2 1 -1 8.