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The systematic solver: forward elimination with partial pivoting (row swaps for stability), then back-substitution. Every row operation is listed — ideal for checking homework.
Row-reduction with partial pivoting; every step shown.
Augmented [A|b] → upper-triangular → back-substitute
| Symbol | Meaning |
|---|---|
| [A|b] | Augmented matrix (coefficients + constants) |
2x+y=5, x+3y=10 → elimination gives y=3, back-substitution x=1.
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Swapping in the largest available pivot each column — avoids division by tiny numbers and improves accuracy.
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Content updated: September 2026