Intersection of a ray and a curved surface

Hi,

I'd like to write a ray tracing program but I have some issues with the mathematics thereof, I'm trying to do some exercises in a book to help me as such but I don't know how to solve e.g. problems of the form:

Find where (if at all) the ray $\displaystyle ray(t) = (5, -1, 0)^T + t(-1, 1, 1)^T$ intersects the curved surface $\displaystyle z(x, y) = (x - 2)(y - 3) + 4$, if there is more than one intersection, which is the first?

As far as I understand I should set the two equations equal to each other and try solve them for the unknown parameter t? I've tried this but I can't get anywhere.