DK-GEORGMOHR 2017 Problem 1

A system of equations $$\begin{cases} x^2 \, ? \, z^2 = -8 y^2 \, ? \, z^2 = 7 \end{cases}$$ is written on a piece of paper, but unfortunately two of the symbols are a little blurred. However, it is known that the system has at least one solution, and that each of the two question marks stands for either $+$ or $-$ . What are the two symbols?