Решите систему уравнений: x^2-8xy+16y^2=25; 4y^2-xy=5.

\[4y^{2} - (4y + 5)y = 5\]

\[4y^{2} - 4y^{2} - 5y = 5\]

\[- 5y = 5\]

\[y = - 1.\]

\[y_{1} = - 1 \Longrightarrow x_{1} = 4 \cdot ( - 1) + 5 =\]

\[= - 4 + 5 = 1.\]

\[2)\ \left\{ \begin{matrix} x - 4y = - 5\ \\ 4y^{2} - xy = 5 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} x = 4y - 5\ \ \ \ \\ 4y^{2} - xy = 5 \\ \end{matrix} \right.\ \]

\[4y^{2} - (4y - 5)y = 5\]

\[4y^{2} - 4y^{2} + 5y = 5\]

\[5y = 5\]

\[y = 1.\]

\[y_{2} = 1 \Longrightarrow \ \ \ \ \ x_{2} = 4 \cdot 1 + 5 =\]

\[= 4 + 5 = 9.\]

\[Ответ:(1;\ - 1);\ \ \ (9;1).\]