$\begin{array}{|l}x^2-y^2=7 \\ x^2+xy+y^2=37\end{array}$ Any suggestions how to solve: $$\begin{array}{|l}x^2-y^2=7 \\ x^2+xy+y^2=37\end{array}$$
I can simplify the system and get a homogeneous polynomial of degree $2$, but I think it must have an easier way.

Another possible approach consists in considering the change of variables $x = r\cos(\theta)$ and $y = r\sin(\theta)$, from whence we get
\begin{align*}
\begin{cases}
r^{2}\cos(2\theta) = 7\\\\
r^{2}(2 + \sin(2\theta)) = 74
\end{cases} \Longleftrightarrow r^{2} = \frac{7}{\cos(2\theta)} = \frac{74}{2+\sin(2\theta)}
\end{align*}
Can you take it from here?
