Решите систему уравнений x-4y=3; xy+3y=9.

Ответ:

\[\left\{ \begin{matrix} x - 4y = 3\ \ \ \\ xy + 2y = 9 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 3 + 4y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (3 + 4y)y + 2y = 9 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 3 + 4y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 3y + 4y² + 2y = 9 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 3 + 4y\ \ \ \ \ \ \ \ \ \ \ \ \\ 4y² + 5y - 9 = 0 \\ \end{matrix} \right.\ \]

\[4y^{2} + 5y - 9 = 0\]

\[D = 25 + 144 = 169\]

\[y_{1} = \frac{- 5 + 13}{8} = 1\]

\[y_{2} = \frac{- 5 - 13}{8} = - 2\frac{1}{4}\]

\[\left\{ \begin{matrix} x = 3 + 4 \cdot 1 \\ y = 1\ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \ или\ \left\{ \begin{matrix} x = 3 - \frac{4 \cdot 9}{4} \\ y = - 2\frac{1}{4}\text{\ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 7 \\ y = 1 \\ \end{matrix} \right.\ \ или\ \left\{ \begin{matrix} x = - 6 \\ y = - 2\frac{1}{4} \\ \end{matrix} \right.\ \]

\[Ответ:(7;1);\ \ \left( - 6;\ - 2\frac{1}{4} \right).\]