What you have to do is augment A to the identity matrix ( [A | I ] ) and then use elementary row operations until you turn A in to I. By doing these row operation on I in the same order you preformed them on A you will end up with the inverse of A (that is [A | I] turns in to [I | A^-1] after using elementary row operations.) Then you can use the inverse to solve the system (turn the system in to its matrix form then multiply both sides by the inverse). I hope that made sense (and helps).