\begin{equation*}
2*x^{2}-xy+y^{2}=4
\end{equation*}
\begin{equation*}
4*x^{2}-5xy+3y^{2}=6
\end{equation*}
Manipulate the two equations so that there is no constant term, and then factorize to get \((2x-y)(x-3y)=0\).
solve([x^3==1], x)
[x == 1/2*I*sqrt(3) - 1/2, x == -1/2*I*sqrt(3) - 1/2, x == 1]