\[\boxed{\text{676.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[x^{2} - y^{2} = 0\]
\[(x - y)(x + y) = 0 \Longrightarrow\]
\[\Longrightarrow \left\lbrack \begin{matrix} x - y = 0 \\ x + y = 0 \\ \end{matrix} \right.\ \Longrightarrow \left\lbrack \begin{matrix} x = y\ \ \ \ \\ x = - y \\ \end{matrix} \right.\ \Longrightarrow\]
\[\Longrightarrow \left\lbrack \begin{matrix} y = x\ \ \ \ \\ y = - x. \\ \end{matrix} \right.\ \]