Since x+y=2, y=2-x and we substitute for y in the other equation:
x2+(2-x)2=9,
x2+4-4x+x2=9,
2x2-4x=9-4=5, divide through by 2:
x2-2x=5/2,
x2-2x+1=5/2+1=7/2,
(x-1)2=7/2, x-1=±√(7/2), x=1±√(7/2), x=2.8708 or -0.8708.
Therefore y=-0.8708 or 2.8708, respectively.