Решите систему уравнений: 6x+y=5; (x-3)(y+5)=2.

Ответ:

\[\left\{ \begin{matrix} 6x + y = 5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (x - 3)(y + 5) = 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = 5 - 6x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (x - 3)(5 - 6x + 5) = 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = 5 - 6x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (x - 3)(10 - 6x) = 2 \\ \end{matrix} \right.\ \]

\[10x - 6x^{2} - 30 + 18x - 2 = 0\]

\[- 6x^{2} + 28x - 32 = 0\ \ \ |\ :( - 2)\]

\[3x^{2} - 14x + 16 = 0\]

\[D = 196 - 192 = 4\]

\[x_{1} = \frac{14 - 2}{6} = 2,\ \ \]

\[x_{2} = \frac{14 + 2}{6} = 2\frac{2}{3}\]

\[\left\{ \begin{matrix} x = 2\ \ \ \\ y = - 7 \\ \end{matrix} \right.\ \ \ \ \ \ или\ \ \ \ \left\{ \begin{matrix} x = 2\frac{2}{3}\text{\ \ \ \ \ \ \ } \\ y = 5 - 16\ \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\ \left\{ \begin{matrix} x = 2\frac{2}{3}\text{\ \ } \\ y = - 11 \\ \end{matrix} \right.\ \]

\[Ответ:(2;\ - 7);\ \ \left( 2\frac{2}{3};\ - 11 \right).\]