Guass-jordan elimination method :

The system of equations are  

Write the equations into matrix form .

Where is coefficient matrix, is variable matrix and is constant matrix.

Solve the equations in Gauss-Jordan method.

The augmented matrix is .

.

The augmented matrix is .

Apply elementary row operations to obtain a reduce the row-echelon form.

Here are represents first row, second row and third row .

Write the corresponding system of the linear equations for the reduced row-echelon form of the augmented matrix is

.

Because the value of  not determined, this system has infinitely many solutions.

Solve for ,  in terms of .

.

where is any real number.

where is any real number.