Решите систему уравнений: 2x+3xy=-20; y-3xy=28.

Ответ:

\[\left\{ \begin{matrix} 2x + 3xy = - 20 \\ y - 3xy = 28\ \ \ \ \ \ \\ \end{matrix}( + ) \right.\ \text{\ \ \ }\]

\[\left\{ \begin{matrix} 2x + y = 8\ \ \ \ \ \\ y - 3xy = 28 \\ \end{matrix}\text{\ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} y = 8 - 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 8 - 2x - 3x(8 - 2x) = 28 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 8 - 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 8 - 2x - 24x + 6x^{2} - 28 = 0 \\ \end{matrix}\text{\ \ \ \ } \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = 8 - 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 6x^{2} - 26x - 20 = 0\ \ \ |\ :2 \\ \end{matrix} \right.\ \]

\[3x^{2} - 13x - 10 = 0\]

\[D = 169 + 120 = 289\]

\[\ x_{1} = \frac{13 - 17}{6} = - \frac{4}{6} = - \frac{2}{3};\ \ \]

\[x_{2} = \frac{13 + 17}{6} = \frac{30}{6} = 5.\]

\[\left\{ \begin{matrix} x = - \frac{2}{3} \\ y = 9\frac{1}{3}\ \\ \end{matrix}\ \ \ \ \ \ или\ \right.\ \text{\ \ \ \ \ \ }\left\{ \begin{matrix} x = 5\ \ \ \\ y = - 2 \\ \end{matrix} \right.\ \]

\[Ответ:\left( - \frac{2}{3};9\frac{1}{3} \right);\ (5; - 2).\]