Решите систему уравнений: x+y=6; xy=8.

\[\left\{ \begin{matrix} x + y = 6 \\ xy = 8\ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 6 - y\ \ \ \ \ \ \\ (6 - y)y = 8 \\ \end{matrix} \right.\ \]

\[6y - y^{2} = 8\]

\[y^{2} - 6y + 8 = 0\]

\[D_{1} = 9 - 8 = 1\]

\[y_{1} = 3 + 1 = 4;\]

\[y_{2} = 3 - 1 = 2;\]

\[x_{1} = 6 - 4 = 2;\]

\[x_{2} = 6 - 2 = 4.\]

\[Ответ:(2;4);(4;2).\]