$\begin{array}{|l}x^2-y^2=7 \\ x^2+xy+y^2=37\end{array}$ 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.

Hint Let 
$$a=x+y \\ b=x-y$$
Then, the equations become 
$$ab=7 \\
3a^2+b^2=4 \cdot 37$$
Thus
$$3a^2+\frac{49}{a^2}=148$$
This is a quadratic in $a^2$.
