Get x and y in quadrat equations system

Question

I need help in solving following system of quadratic equations :

$$ 2x^2+y^2=4$$ $$2xy-2x=-5$$

I used every known me equations solving methods, but no was helpful for me... Can you help me by giving step-by-step solution (that is homework and I really need it...) ? Thanks in advance !

Answer 1

There are no real solutions. The resultant of $2 x^2 + y^2 - 4$ and $2 x y-2 x+5$ with respect to $x$ is $4\,{y}^{4}-8\,{y}^{3}-12\,{y}^{2}+32\,y+34$, which has no real roots.

Answer 2

HINT:

From the second equation we have, $2x(y-1)=-5,x=\frac{5}{2(1-y)}$

Put the $x$ in the first