Guass-jordan elimination method :

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 equation for the reduced row-echelon form of the augmented matrix is

.

Because the value of  not determined, this system has infinetly many solutions.solving for ,  in terms of . .

The solution of the system is where is any real number.

The solution of the system is where is any real number.