# Online Calculator for 3x3 linear equation systems

## Calculator linear equations

Solving of the equation system with Cramers Rule, Gaussian Method and Gauss-Jordan approach.

The solver calculates the solution of the equation system step by step with the Cramers Rule and the Gaussian Method.

### Linear equation system with three equations and the three unknowns x, y and z

$\begin{array}{c}{a}_{11}x+{a}_{12}y+{a}_{13}z={b}_{1}\\ {a}_{21}x+{a}_{22}y+{a}_{23}z={b}_{2}\\ {a}_{31}x+{a}_{32}y+{a}_{33}z={b}_{n}\end{array}$

Enter the coefficients: a_{11}, a_{12}, ... and b_{1}, ...

### Cramer's rule

Solve of the equation system with Cramer's rule. A step by step calculator for solving 3x3 determinats is here: Solver 3x3 determinants

### Gauss algorithm

Solve of the equation system with Gaussian method. The Gaussian method transforms the matrix in row echelon form.

The entered coefficient matrix is:

### Calculation of the row echelon form (Gauss method)

### Solution by backward insertion

### Alternative calculation using the reduced row echelon form (Jordan method)

The solution of the equation system is now in the right column of the coefficient matrix and can be read directly.