I want to solve this system equations. I found 2 solutions, but it's was effort algebra with the second equation and take $z=0$ in (1), you can see 2 solutions with $x=-2,2$ and $ y=1,-1$. $ (1) \ x^2+xyz+5z^3=4\\ (2) \ 3x^2-y^2+5xy=2 $
Are you know any algorithm, or method, or technique to find others solutions (?) I think that this system eq, have not other solutions in $\mathbb{R}$