Решите систему уравнений: y+2x=-5; x^2+y^2=25.

\[\left\{ \begin{matrix} y + 2x = - 5\ \\ x^{2} + y^{2} = 25 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = - 2x - 5 \\ x^{2} + y^{2} = 25 \\ \end{matrix} \right.\ \]

\[x^{2} + ( - 2x - 5)^{2} = 25\]

\[x^{2} + 4x^{2} + 20x + 25 - 25 = 0\ \]

\[5x^{2} + 20x = 0\]

\[5x(x + 4) = 0\]

\[x_{1} = 0;\ \ \ \ x_{2} = - 4.\]

\[x_{1} = 0 \Longrightarrow \ \ \ \ \ \ y_{1} = - 2 \cdot 0 - 5 =\]

\[= 0 - 5 = - 5.\]

\[x_{2} = - 4 \Longrightarrow \ \ y_{2} =\]

\[= - 2 \bullet ( - 4) - 5 = 8 - 5 = 3.\]

\[Ответ:(0;\ - 5),\ \ \ ( - 4;3).\]