Решите систему уравнений:3x+7y=-5; 5x+4y=7.

Ответ:

\[\left\{ \begin{matrix} 3x + 7y = - 5\ \ \ | \cdot 5\ \ \ \ \ \\ 5x + 4y = 7\ \ \ | \cdot ( - 3) \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} 15x + 35y = - 25\ \ \ \ \ \ (1) \\ - 15x - 12y = - 21\ \ (2) \\ \end{matrix} \right.\ \]

\[23y = - 46\ \ \]

\[y = - 2\]

\[\left\{ \begin{matrix} y = - 2\ \ \ \ \ \ \ \ \ \ \ \ \\ 3x + 7y = - 5 \\ \end{matrix}\ \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} y = - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3x = - 5 - 7y \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = - 2\ \ \ \ \ \ \ \ \ \ \ \ \\ x = - \frac{5}{3} - \frac{7}{3}y \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = - 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = - \frac{5}{3} - \frac{7}{3} \cdot ( - 2) \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\ \left\{ \begin{matrix} y = - 2\ \ \ \ \ \ \ \ \ \ \ \\ x = - \frac{5}{3} + \frac{14}{3} \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = - 2\ \ \ \ \ \ \\ x = \frac{9}{3} = 3 \\ \end{matrix} \right.\ \]

\[Ответ:(3;\ - 2).\]