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

\[\left\{ \begin{matrix} x² - 4xy + 4y^{2} = 25 \\ x + 2y = 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} (x - 2y)^{2} = 25 \\ x = 3 - 2y\ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

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

\[\left\{ \begin{matrix} 2x = 8\ \ \ \ \ \\ y = \frac{3 - x}{2} \\ \end{matrix} \right.\ \ \Leftrightarrow \left\{ \begin{matrix} 2x = - 2\ \ \\ y = \frac{3 - x}{2} \\ \end{matrix} \right.\ \]

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

\[Ответ:\ \ (4;\ - 0,5);\ \ ( - 1;2).\]