\[\left\{ \begin{matrix} x + y = 7\ \ \ \\ 2x + y = 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\left\{ \begin{matrix} y = 7 - x\ \ \ \ \ \ \ \ \ \\ 2x + 7 - x = 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\left\{ \begin{matrix} y = 7 - x \\ x = 1\ \ \ \ \ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x = 1\ \ \ \ \ \ \ \\ y = 7 - 1 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x = 1 \\ y = 6 \\ \end{matrix} \right.\ \]
\[Проверка:\ \]
\[\left\{ \begin{matrix} 1 + 6 = 7\ \ \ \ \ \ \\ 2 \cdot 1 + 6 = 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 7 = 7 \\ 8 = 8 \\ \end{matrix} \right.\ \Longrightarrow верно.\]
\[Ответ:(1;6).\]