\[\left\{ \begin{matrix} x + y = 5\ \ \ (1) \\ x - y = 7\ \ \ (2) \\ \end{matrix} \right.\ \]
\[(1) + (2) \Longrightarrow 2x = 12\]
\[\left\{ \begin{matrix} 2x = 12\ \ \\ x + y = 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x = 6\ \ \ \ \ \ \ \ \\ y = 5 - x \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x = 6\ \ \ \ \ \ \ \ \\ y = 5 - 6 \\ \end{matrix} \right.\ \text{\ \ \ \ }\]
\[\left\{ \begin{matrix} x = 6\ \ \ \\ y = - 1 \\ \end{matrix} \right.\ \]
\[Ответ:(6;\ - 1).\]