$\displaystyle x=zx+zy $

$\displaystyle y=zx+2zy $

$\displaystyle x^2+2xy+y^2=100$

Is this system solvable? I can solve for z in terms of x and y, but I can't separate x and y to get a solution. Its three unkowns and three equations, but I don't know if all three unkowns have to be in all three equations. Anyway, if I solve for z I get $\displaystyle x^2+xy=y^2$ but that's as far as I can get. Any suggestions?

Thanks