\[\left\{ \begin{matrix} 5x - y = 23\ \ \\ 5x + 2y = 14 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = 5x - 23\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 5x + 2 \cdot (5x - 23) = 14 \\ \end{matrix} \right.\ \]
\[5x + 10x - 46 = 14\]
\[15x = 14 + 46\]
\[15x = 60\]
\[x = 4.\]
\[y = 5x - 23 = 5 \cdot 4 - 23 = - 3.\]
\[\left\{ \begin{matrix} x_{0} = 4\ \ \ \\ y_{0} = - 3 \\ \end{matrix} \right.\ \]
\[x_{0} + y_{0} = 4 - 3 = 1.\]
\[Ответ:1)\ 1.\]