System of Linear Equations Solver

It solves square systems of linear equations with two or three unknowns, written as a 2x2 or 3x3 set of coefficients with a constant on the right of each equation. It does not handle more than three unknowns or non-linear terms.

It applies Gauss-Jordan elimination with partial pivoting. The coefficients and constants form an augmented matrix that is reduced to row echelon form, then the solution is read off directly. Partial pivoting keeps the arithmetic numerically stable.

If the equations contradict each other, such as x + y = 1 and x + y = 2, the system is inconsistent and has no solution. If an equation is just a multiple of another, such as x + y = 1 and 2x + 2y = 2, the system is dependent and has infinitely many solutions.

Solutions are computed with floating point math and rounded to six decimal places for display. Exact fractions like one third appear as 0.333333. Whole-number answers are shown without trailing zeros.

Yes. Coefficients and constants can be any finite number, including negatives, zero and decimals. A zero leading coefficient is fine because partial pivoting reorders the equations automatically.

Yes. The solver runs entirely in your browser. The coefficients and constants you enter are never uploaded or stored on a server, so your calculations stay on your device.