๐Ÿ”ขSystem of Equations Solver

Solve 2ร—2 and 3ร—3 systems of linear equations with full step-by-step Gaussian elimination working, exact fractions, and special-case handling.

x + y =
x + y =
x + y + z =
x + y + z =
x + y + z =

Step-by-step working

Free System of Equations Solver with Steps

Stuck on a simultaneous equations problem? Our free system of equations solver handles 2ร—2 and 3ร—3 linear systems and shows every step of the working, so you understand the method โ€” not just the answer. Enter the coefficients in the clean grid, and get the values of each variable clearly displayed, followed by a full elimination walkthrough.

It uses Gaussian elimination with partial pivoting under the hood, so it handles awkward systems correctly โ€” including those with fractional answers, which are shown as proper fractions rather than rounded decimals. Special cases are explained too: if the system has no solution or infinitely many, you'll see exactly why, with the contradiction or parametric form shown. A verification step substitutes the answer back into each equation to confirm it's correct.

Simply enter your coefficients to solve instantly. No sign-up, no downloads, no limits โ€” just clear, step-by-step solutions.