Решите систему уравнений y+2x=5; 2x-xy=-1.

Ответ:

\[\left\{ \begin{matrix} y + 2x = 5\ \ \ \ \ \ \\ 2x - xy = - 1 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} y = 5 - 2x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ 2x - x(5 - 2x) = - 1 \\ \end{matrix} \right.\ \]

\[2x - 5x + 2x^{2} + 1 = 0\]

\[2x^{2} - 3x + 1 = 0\]

\[D = 9 - 8 = 1\]

\[x_{1} = \frac{3 + 1}{4} = 4;\ \ \ x_{2} = \frac{3 - 1}{4} = \frac{1}{2}\]

\[\left\{ \begin{matrix} x = 4\ \ \ \\ y = - 3 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = \frac{1}{2} \\ y = 4 \\ \end{matrix} \right.\ \]

\[Ответ:(4;\ - 3);\ \ (0,5;4).\]