You don't need 3 equations to get a general solution. To do this use the equations x-3y-z=0 and -x+2y+0z= -3. Start out by letting z = t. Then solving those 2 equations simultaneously, your x's cancel out leaving you with -y-z=-3. But since z=t, then -y=-3+t or y=3-t. Now sub that in for y in the first equation, along with the fact that z=t to get x-3(3-t)-t = 0 and solve for x. x=9-2t. So a general solution for this would be (9-2t, 3-t, t)
