The first step in the Gauss-Jordan method is to write an augmented coefficient matrix for the system of equations. Columns of the matrix correspond to variables -- usually x, y, and z -- while rows represent different equations.
The second step involves the use of elementary row operations to transform the coefficient matrix into diagonal form. A matrix in diagonal form has zeros both above and below the diagonal of the matrix. If you are unable to transform the matrix into diagonal form, the system has no solution or infinite solutions.
The final step is to make each diagonal element equal to one. This is accomplished by dividing every row of the matrix by that row's diagonal element. The solution for each variable is found in the fourth column of the matrix. For example, to find the value of "x," you would find the row where the coefficient of x is 1. The value in the fourth column of that row is the value of x.