Решите систему уравнений: y+3x=-5; x^2+y^2=25.

\[\left\{ \begin{matrix} y + 3x = - 5 \\ x^{2} + y^{2} = 25 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\left\{ \begin{matrix} y = - 3x - 5 \\ x^{2} + y^{2} = 25 \\ \end{matrix} \right.\ \]

\[x^{2} + ( - 3x - 5)^{2} = 25\]

\[x^{2} + 9x^{2} + 30x + 25 - 25 = 0\]

\[10x^{2} + 30x = 0\]

\[10x(x + 3) = 0\]

\[x_{1} = 0;\ \ \ \ x_{2} = - 3.\]

\[x_{1} = 0 \Longrightarrow \ \ \ \ \ \ \ \ \ y_{1} = - 3 \bullet 0 - 5 =\]

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

\[x_{2} = - 3 \Longrightarrow \ \ \ \ \ y_{2} =\]

\[= - 3 \cdot ( - 3) - 5 = 9 - 5 = 4.\]

\[Ответ:(0;\ - 5),\ \ \ ( - 3;4).\]