I was given this task and I solved it, but only after solving for $x^4+x^3$... $$x^2+y^2+4z^2=6y-4\quad \& \quad 2xy-4xz+4yz=y^2+5$$
How I tried: 1. I summed (and multiplying the second one with $-1$) the two equations, getting: $$(x-y+z)^2=-(y-3)^2 \implies y-3=0 \quad \& \quad x-y+z=0$$
I than put $y$ into the equations but in the end I got something long with $x^4$...
I know this task is not ment to solve polynomials, so I am asking for a simpler solution.