You're correct, a transformation has to be from n to n variables. (it has to be a -diffeomorphism)
Thus just make the following transformation : (u,v,w) -> (y,z,w), then integrate with respect to w to get the "marginal" pdf of (y,z)
A question from my homework asks if u,v,w are iid exponentially and y=u/w and z=v/w find the pdf of (y,z). I know generally how to do transformations but in this case I cant find a Jacobian since the transformation is from 3 to 2 variables. How would I go about solving this problem.