System of Equations Solver

The System of Equations Solver handles two or more equations sharing unknowns. Linear systems of two to six variables. Nonlinear pairs such as a line and a circle. It selects substitution when one variable is already isolated, elimination when coefficients line up, and Gaussian elimination on an augmented matrix for three or more unknowns. It detects inconsistent systems and reports no solution, and detects dependent systems and reports the solution as a parameter family. Each case is explained with the row or the substitution that revealed it. Word problems that translate to a system, such as mixture, rate, or cost problems, are set up first with each variable defined before any solving begins.

Enter the equations separated by commas, the word "and", or new lines. 2x + y = 7 and x - y = -1. A photo of the system works, including handwritten braces. If the assignment names a method, write it before the system: "solve by elimination". Keep every equation in the same variables and make sure each one is complete. The Answer form option sets whether the values come back exact or rounded. For a system with more equations than unknowns, the solver checks consistency and reports whether a solution exists. For a word problem, define the variables in a line at the top or let the solver define them and echo the definitions back for you to confirm.

The output shows the solution as an ordered pair or triple, then the method: which equation was substituted or scaled, what was added to what, each resulting equation, and the back-substitution. Matrix solutions show each row operation with its label. A final check plugs the values into every original equation. The working is shown so you can check it. For a single equation, use the Equation Solver. To invert or multiply matrices on their own, use the Matrix Calculator. Ask a follow-up to see the same system solved by another method, or to add a third equation and rerun. The final check is written as substitutions, so a sign error in any equation would show up there.