About this tool
Solve a system of two or three linear equations in two or three unknowns. Pick 2x2 or 3x3, type the coefficients, and the solver returns the values of x, y (and z), the determinant of the coefficient matrix, and whether the system has a unique solution, no solution, or infinitely many. Everything runs locally in your browser and updates as you type.
The method is Cramer's rule. For a 2x2 system a1x+b1y=c1, a2x+b2y=c2 the main determinant is D = a1b2 - a2b1, then x = (c1b2 - c2b1)/D and y = (a1c2 - a2c1)/D. The 3x3 case replaces each column of the coefficient matrix with the constants and divides that determinant by D. When D = 0 the system is not uniquely solvable, and the tool inspects the replaced-column determinants to tell a dependent (infinitely many) system apart from an inconsistent (no solution) one.
Enter each coefficient exactly as it appears, using negative numbers where needed. Rearrange your equations into the ax + by = c form first so the columns line up with the input boxes.