System of Equations Calculator

Solving Systems of Linear Equations

This calculator solves a system of three linear equations in three unknowns (x, y, z) using Cramer's Rule, a determinant-based method for finding unique solutions.

Formula

x = det(Aỿ) ÷ det(A), and similarly for y and z, where A is the coefficient matrix and Aỿ replaces the corresponding column with the constants.

How to Use This Calculator

• Enter the coefficients (a, b, c) and constant (d) for each of your three equations.
• Click "Solve System" to get the values of x, y, and z.

Example

The system x+y+z=6, 2y+5z=-4, 2x+5y-z=27 solves to x=5, y=3, z=-2.