\[\boxed{\text{1088.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[\textbf{а)}\ \left\{ \begin{matrix} 3x + 4y = 0 \\ 2x + 3y = 1 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 3x = - 4y \rightarrow x = - \frac{4}{3}y\ \ \ (1) \\ 2 \cdot \left( - \frac{4}{3}y \right) + 3y = 1\ \ \ \ \ \ \ (2) \\ \end{matrix} \right.\ \]
\[(1)\ - \frac{8}{3}y + 3y = 1\]
\[\frac{9}{3}y - \frac{8}{3}y = 1\]
\[\frac{1}{3}y = 1\]
\[y = 3\]
\[(2)\ \ \ x = - \frac{4}{3} \cdot 3\]
\[x = - 4\]
\[Ответ:( - 4;3).\]
\[\textbf{б)}\ \left\{ \begin{matrix} 7x + 2y = 0 \\ 4y + 9x = 10 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 2y = - 7x \rightarrow y = - 3,5x\ \ (2) \\ 4 \cdot ( - 3,5x) + 9x = 10\ \ \ \ \ (1) \\ \end{matrix} \right.\ \]
\[(1)\ - 14x + 9x = 10\]
\[- 5x = 10\]
\[x = - 2\]
\[(2)\ \ \ y = - 3,5 \cdot ( - 2)\]
\[y = 7\]
\[Ответ:( - 2;7).\]
\[\textbf{в)}\ \left\{ \begin{matrix} 5x + 6y = - 20 \\ 9y + 2x = 25\ \ \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 5x = - 20 - 6y \\ 9y + 2x = 25 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} x = - 4 - 1,2y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2) \\ 9y + 2 \cdot ( - 4 - 1,2y) = 25\ \ \ (1) \\ \end{matrix} \right.\ \]
\[(1)\ \ 9y - 8 - 2,4y = 25\]
\[6,6y = 33\]
\[y = 5\]
\[(2)x = - 4 - 1,2 \cdot 5\]
\[x = - 10\]
\[Ответ:( - 10;5).\]
\[\textbf{г)}\ \left\{ \begin{matrix} 3x + 1 = 8y\ \ \ \ \ \ \ \\ 11y - 3x = - 11 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} 3x = 8y - 1 \rightarrow x = \frac{8}{3}y - \frac{1}{3}\ \ \ \ (2) \\ 11y - 3 \cdot \left( \frac{8}{3}y - \frac{1}{3} \right) = - 11\ \ \ \ \ \ \ (1) \\ \end{matrix} \right.\ \]
\[(1)\ \ \ 1y - 8y + 1 = - 11\]
\[3y = - 12\]
\[y = - 4\]
\[(2)\ \ \ \ x = \frac{8}{3} \cdot ( - 4) - \frac{1}{3}\]
\[x = - \frac{32}{3} - \frac{1}{3} = - \frac{33}{3} = - 11\]
\[Ответ:( - 11;\ - 4).\]