Решите систему уравнений x+8y=-6; 5x-2y=12.

Ответ:

\[\left\{ \begin{matrix} x + 8y = - 6\ \ \ \ \ \ \ \ \ \ \ \ \\ 5x - 2y = 12\ \ \ | \cdot 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x + 8y = - 6\ \ \ \ \ \ \ \ (1) \\ 20x - 8y = 48\ \ \ \ (2) \\ \end{matrix} \right.\ \]

\[(1) + (2) \Longrightarrow 21x = 42\ \ \]

\[\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = 2.\]

\[\left\{ \begin{matrix} x = 2\ \ \ \ \ \ \ \ \ \ \\ y = \frac{5}{2}x - 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = \frac{5}{2} \cdot 2 - 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 2\ \ \ \ \ \ \ \\ y = 5 - 6 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 2\ \ \ \\ y = - 1 \\ \end{matrix} \right.\ \]

\[Ответ:(2;\ - 1).\]