\(1,\Leftrightarrow\left(x^2-2xy+y^2\right)+\left(x^2-6x+9\right)=0\\ \Leftrightarrow\left(x-y\right)^2+\left(x-3\right)^2=0\\ \Leftrightarrow x=y=3\\ 2,\Leftrightarrow\left(x^2+2xy+y^2\right)+\left(y^2+6y+9\right)=0\\ \Leftrightarrow\left(x+y\right)^2+\left(y+3\right)^2=0\\ \Leftrightarrow\left\{{}\begin{matrix}x+y=0\\y=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=-3\end{matrix}\right.\)