System of Equations Solver: Step-by-Step Solution Online

Solve 2 or 3 linear equation systems by substitution, elimination, Cramer or matrix. Detailed steps and graph.

2 equations, 2 unknowns

① x + y =

② x + y =

Examples: 2x+y=5 / x−y=1 3x+2y=12 / x−y=1 x+y=4 / 2x−y=2 ∞ solutions ∅ sans solution x=3, y=5

Solving method

↵ Enter to solve

Enter the coefficients and click Solve.

How to solve a system of equations?

A system of linear equations is a set of equations sharing the same unknowns. The solution is the set of values that simultaneously satisfy all equations. Depending on the case, a system may have a unique solution, infinitely many solutions, or no solution.

Substitution method

Isolate one unknown in one equation, then substitute into the others. Simple but can become complex with fractions. Ideal for 2×2 systems with simple coefficients.

Gaussian elimination and Cramer's rule

Gaussian elimination combines equations to progressively eliminate unknowns. Cramer's rule uses determinants: x = Det(Aₓ)/Det(A), y = Det(Aᵧ)/Det(A). These methods are systematic and apply to 2×2 and 3×3 systems.

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