Solve this system of equations for real numbers Solve this system of equations for real numbers:
$$x^2+xy=3, $$
$$4y^2+3xy=22. $$
I think it's pretty obvious what to do to start, I think we should sum the two equations and get that:
$$x^2+4xy+4y^2=25$$
$$(x+2y)^2=5^2$$
$$\Rightarrow x+2y=5,-5$$
I'm not sure where to go from here, I've tried factorizing the equations and substituting what we've got but I've not gotten anywhere. Hints are appreciated.

Hint:
As $xy\ne0$ and both the equations are of the same degree, WLOG set $y=mx$ so that $$3=x^2(1+m)\  \   \  \  (1)$$
$$\dfrac{22}3=\dfrac{(4m^2+3m)x^2}{(1+m)x^2}$$
We can solve for $m$ and use the values in $(1)$
