The table below is the row reduction process applied simultaneously to the system of equations and its associated augmented matrix. In practice, one does not usually deal with the systems in terms of equations, but instead makes use of the augmented matrix, which is more suitable for computer manipulations. The row reduction procedure may be summarized as follows: eliminate from all equations below , and then eliminate from all equations below . This will put the system into triangular form. Then, using back-substitution, each unknown can be solved for.
