When using matrices to solve systems of equations, remember we can interchange rows, add or subtract rows to form new rows, multiply rows and add to other rows or divide rows and add to other rows. All of this is in an attempt to get the matrix into a form where we can solve for the variables in the equations of the system. One form is seen above.  Suppose the variables in the system are x, y, z. Then z = f. Substitute f for z in the second equation to solve for y and then substitute that value for y into the first equation and solve for x.