Is there a way I can find a parametric (rational) solution to the following system:
$$\begin{cases}& x^2-y^2 = 2\\ &8x^2-z^2 = 7 \end{cases}.$$
I know a solution $(x,y) = (\frac{p^2+2q^2}{2pq}, \frac{p^2-2q^2}{2pq})$ satisfies the first equation alone.
Thank you for the feedback.