Calculateur de systèmes d'équations

Paste your equations and the calculator reads each line the way you wrote it: left side, equals sign, right side. It expands any brackets, clears fractions, and moves every unknown to the left so each line lands in the standard form ax + by = c. Those coefficients are kept as exact fractions, which is why a third stays 1/3 instead of drifting into 0.3333.

The rows then go into an augmented matrix and the solver runs Gauss-Jordan elimination. It picks a pivot in the first column, favouring one worth 1 or −1 so the printed arithmetic stays readable, divides that row down to a single unknown, and subtracts multiples of it from every other row. It repeats this column by column until each unknown sits alone in its own row.

What comes out tells you which of three things happened. If every unknown gets its own pivot, there is exactly one answer, and the calculator substitutes it back into your original equations to prove it. If a row collapses to 0 = 5, the equations contradict each other and nothing can satisfy them. If a row collapses to 0 = 0, one equation repeated another, so the calculator names the free unknowns and writes the rest in terms of them.

Square systems also get their determinant and the Cramer's rule numerators. Systems with two unknowns get a graph of both lines. All of it runs in your browser.