System of Equations Solver

A systematic way to solve linear systems: write them as an augmented matrix, then use row operations to clear entries below each pivot until the matrix is triangular — then read the answers off from the bottom row up (back-substitution).

The equations describe the same line (in 2D) or overlapping planes (in 3D), so every point on it satisfies all of them. One variable stays free — it can be anything, and the others follow from it.

That's partial pivoting: before eliminating a column, the row with the largest entry becomes the pivot row. It keeps rounding error small and handles a zero pivot gracefully — for example, 0x + y = 2.

Elimination produces a row like 0 = 5 — a contradiction. Geometrically that's parallel lines (2×2) or planes with no common point (3×3).

No. The elimination runs entirely in your browser — nothing is sent to a server or stored.