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

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

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

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

\[(3 - 4y)^{2} = 25\]

\[1)\ 3 - 4y = 5\]

\[- 4y = 2\]

\[y = - 0,5;\]

\[x = 3 - 2y = 3 + 1 = 4.\]

\[2)\ 3 - 4y = - 5\]

\[- 4y = - 8\]

\[y = 2;\]

\[x = 3 - 2y = 3 - 4 = - 1.\]

\[Ответ:(4; - 0,5);( - 1;2).\]