Ive differentiated to find three equations

2x - 2ux - uy = 0

2y - ux - 2uy = 0

-(x^2 + xy + y^2 - 3) = 0

and need to find all solutions of x,y, and u. Ive solved for u and found x, y, u, are (1,1, 2/3) (-1,-1,2/3) but cannot find the other two solutions. Any help with that would be much appreciated, thought it had to do with completing the square but I guess not.