Решите систему уравнений: 4y+x=2; (x-4)(y+3)=4.

Ответ:

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

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

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

\[\left\{ \begin{matrix} x = 2 - 4y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - 4y^{2} - 12y - 2y - 6 - 4 = 0 \\ \end{matrix}\text{\ \ } \right.\ \text{\ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 2 - 4y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - 4y^{2} - 14y - 10 = 0\ \ \ |\ :( - 2) \\ \end{matrix}\text{\ \ \ \ } \right.\ \]

\[2y^{2} + 7y + 5 = 0\]

\[D = 49 - 40 = 9\]

\[Ответ:(6;\ - 1);\ (12;\ - 2,\ 5)\text{.\ }\]