The system of equations are .

If we let , and

The original system of equations can be written compactly as the matrix equation

                 (Multiply each side by )

             (Apply associative property of multiplication)

                       ()

                             (Apply identity property of matrix: )

Now we find

Form the matrix

     ()

              ()

              ()

    ()

    ()

    ()

The matrix  is now in reduced row echelon form, and the identity matrix  is

on the left of the vertical bar. The inverse of A is

             (Equate the each side corresponding entries)

The solution is or, using an ordered pair is .