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

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

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

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

\[5x² - 20x = 0\]

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

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

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

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

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

\[= 8 - 5 = 3.\]

\[Ответ:(0;\ - 5),\ (4;3).\]