Решите систему уравнений: 8x+3y=31; 6x-5y=45.

\[\left\{ \begin{matrix}
8x + 3y = 31\ \ | \cdot 3 \\
6x - 5y = 45\ \ | \cdot 4\ \\
\end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix}
24x + 9y = 93\ \ \ \ \ \\
24x - 20y = 180 \\
\end{matrix} \right.\ - \ \ \ \ \]

\[\left\{ \begin{matrix}
29y = - 87\ \ \\
x = \frac{45 + 5y}{6} \\
\end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix}
y = - 3 \\
x = 5\ \ \ \\
\end{matrix} \right.\ \]

\[Ответ:(5;\ - 3).\]