\(2x^3+2x^2y-xy-y^2+x+y=0\)
\(\Leftrightarrow2x^2\left(x+y\right)-y\left(x+y\right)+x+y=0\)
\(\Leftrightarrow\left(x+y\right)\left(2x^2-y+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}y=-x\\y=2x^2+1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x^3+2x^2=4\\2x^3-x\left(2x^2+1\right)+x^2=4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^3+x^2-2=0\\x^2-x-4=0\end{matrix}\right.\)