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

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

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

\[5y = 5\]

\[y = 1.\]

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

\[= 5 - 4 = 1.\]

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

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

\[- 5y = 5\]

\[y = - 1.\]

\[y_{2} = - 1 \Longrightarrow x_{2} =\]

\[= - 5 - 4 \cdot ( - 1) = - 5 + 4 = - 1.\]

\[Ответ:(1;1),\ \ \ ( - 1;\ - 1).\]