$G_1(x, y_1(x), y_2(x)) = 0$
$G_2(x, y_1(x), y_2(x)) = 0$
Since $G_1$ and $G_2$ are composite functions I can use the chain rule and split them up into partial derivatives. The derivative of both functions should be $0$ since they are both horizontal lines. I'm not sure what to do after that. Maybe just substitution?