Решите систему уравнений 4x^2+4xy+y^2=25; 2x-y=3.

Ответ:

\[\left\{ \begin{matrix} 4x^{2} + 4xy + y^{2} = 25 \\ 2x - y = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 2x - 3\ \ \ \ \ \ \ \\ (2x + y)^{2} = 25 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 2x - 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (2x + 2x - 3)^{2} = 25 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 2x - 3\ \ \ \ \ \ \ \\ (4x - 3)^{2} = 25 \\ \end{matrix} \right.\ \]

\[4x - 3 = 5\ \ \ \ \ 4x - 3 = - 5\]

\[4x = 8\ \ \ \ \ \ \ \ \ \ \ \ \ 4x = - 2\]

\[x = 2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x = - 0,5\]

\[\left\{ \begin{matrix} x = 2 \\ y = 1 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = - 0,5 \\ y = - 4\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:(2;1);\ \ ( - 0,5;\ - 4).\]