[tex]x+y=2\\y=-x+2\\\\x^2+y^2=2\\x^2+(-x+2)^2=2\\x^2+x^2-4x+4=2\\2x^2-4x+4-2=0\\2x^2-4x+2=0\ \ \ |:2\\x^2-2x+1=0\\(x-1)^2=0\\x-1=0\\x=1\\\\y=-x+2=-1+2=1\\\\x=y=1[/tex]
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[tex]x+y=2\\y=-x+2\\\\x^2+y^2=2\\x^2+(-x+2)^2=2\\x^2+x^2-4x+4=2\\2x^2-4x+4-2=0\\2x^2-4x+2=0\ \ \ |:2\\x^2-2x+1=0\\(x-1)^2=0\\x-1=0\\x=1\\\\y=-x+2=-1+2=1\\\\x=y=1[/tex]