Решите систему уравнений: a+2b=5; 3a-b=8.

\[\left\{ \begin{matrix} a + 2b = 5\ \ \ \ \ \ \ \ \ \\ 3a - b = 8\ \ | \cdot 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} a + 2b = 5\ \ \ \ \ \\ 6a - 2b = 16 \\ \end{matrix} \right.\ \ ( + )\]

\[7a = 21\]

\[a = 3.\]

\[\left\{ \begin{matrix} a = 3\ \ \ \ \ \ \ \ \ \ \ \\ b = 3a - 8 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[b = 3 \cdot 3 - 8 = 1.\]

\[\left\{ \begin{matrix} a = 3 \\ b = 1 \\ \end{matrix} \right.\ \]

\[Ответ:(3;1)\text{.\ }\]