Решите систему уравнений:5x+8y=-1; x+2y=4.

Ответ:

\[\left\{ \begin{matrix} 5x + 8y = - 1\ \ \ \ \ \ \ \ \ \ \ \\ x + 2y = 4\ \ \ | \cdot ( - 4) \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} 5x + 8y = - 1\ \ \ \ \ \ \ \ \ \ \ (1) \\ - 4x - 8y = - 16\ \ \ \ (2) \\ \end{matrix} \right.\ \]

\[x = - 17\]

\[\left\{ \begin{matrix} x = - 17\ \ \ \ \ \\ x + 2y = 4 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = - 17\ \ \ \ \\ 2y = 4 - x \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} x = - 17\ \ \ \ \ \\ y = 2 - \frac{1}{2}x \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} x = - 17\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ y = 2 - \frac{1}{2} \cdot ( - 17) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = - 17\ \ \ \ \\ y = \frac{4}{2} + \frac{17}{2} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = - 17 \\ y = \frac{21}{2}\text{\ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = - 17 \\ y = 10,5 \\ \end{matrix} \right.\ \]

\[Ответ:( - 17;10,5).\]