System of Equations Solver

What is the System of Equations Solver?

The System of Equations Solver solves a system of two unknowns x and y. The calculator uses Cramer’s rule and shows a verification that the solution satisfies both equations.

The calculator is free, works in your browser without registration, and displays the result as soon as you change the values. The calculations are done on your own device, and the data you enter is not sent anywhere.

Formula and Calculation Principle

Determinant D = a₁b₂ − a₂b₁. If D ≠ 0, then x = (c₁b₂ − c₂b₁) / D and y = (a₁c₂ − a₂c₁) / D.

Practical Example

2x + 3y = 13 and x − y = 1: D = −5, x = 3.2 and y = 2.2. With default values, the calculator gives the result: Solution x = 3.2000, y = 2.2000.

Who is the calculator suitable for?

For high school and university students and anyone who needs a quick check of a system of equations solution.

Tips and Notes

• Rewrite all terms in the form ax + by = c before entering.
• Check the solution by substituting it back into the original equations.
• For negative coefficients, use a minus sign.