How do you go about finding (x,y,z)? I can't find this in my textbook.
I would prefer Ackbeet's method. Since z does not appear in the first equation and x does not appear in the second, it is easy to solve the two equations for x and z in terms of y. Then you can use "y" as parameter. Once you have x= f(y) and z= g(y), your parametric equations for the line of intersection are x= f(t), y= t, z= g(t).