Actually, it is the other way around- row reduce in order to get the echelon form.

The "augmented matrix" for this system is .

Now use row operations to put this into echelon form. For example, a first step would be to subtract three times the first row from the second row and subtract two times the first row from the third row:

That take care of the first row. Now subtract 3/7 times the second row from the third row.