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.