x+y+z=4 2xy-z^2=16 z=4-(x+y) 2xy-16+8(x+y)-(x+y)^2=16 2xy-16+8(x+y)-x^2-2xy-y^2=16 -x^2-y^2+8(x+y)=32 (-x^2+8x-16)+(-y^2+8y-16)=0 -(x-4)^2-(y-4)^2=0 -(x-4)^2=(y-4)^2 x-4=0 y-4=0 x=4 y=4 z=-4 x+y+2z=0