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

Solving complex systems of equations can quickly become a technical headache, especially if you are concerned about the confidentiality of your calculations. Our free system of equations solver offers a 100% client-side solution, processing your data locally in your browser with no storage on our servers. You benefit from impeccable mathematical precision and immediate execution in complete security. Simplify your academic or professional work with a reliable, fast tool designed to ensure the total protection of your information.

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.

Tools in the same category

Derivative Calculator Statistics Calculator GCD and LCM Calculator Fraction Calculator Multiplication Tables Math Solver