\[\left\{ \begin{matrix} 5a - 3b = 14 \\ 2a + b = 10\ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} b = 10 - 2a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 5a - 3 \cdot (10 - 2a) = 14 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]
\[\left\{ \begin{matrix} b = 10 - 2a\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 5a - 30 + 6a = 14 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} b = 10 - 2a \\ 11a = 44\ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} a = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ b = 10 - 2 \cdot 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} a = 4 \\ b = 2 \\ \end{matrix} \right.\ \]
\[Проверка:\ \]
\[\left\{ \begin{matrix} 5 \cdot 4 - 3 \cdot 2 = 14 \\ 2 \cdot 4 + 2 = 10\ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 14 = 14 \\ 10 = 10 \\ \end{matrix} \right.\ \Longrightarrow верно.\]
\[Ответ:(4;2).\]