Решите систему уравнений: x-2y=4; xy=6.

Ответ:

\[\left\{ \begin{matrix} x - 2y = 4 \\ xy = 6\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 4 + 2y\ \ \ \ \ \ \\ (4 + 2y)y = 6 \\ \end{matrix} \right.\ \]

\[4y + 2y^{2} = 6\]

\[2y^{2} + 4y - 6 = 0\ \ \ |\ :2\]

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

\[D_{1} = 1 + 3 = 4\]

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

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

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

\[x_{2} = 4 + 2 \cdot ( - 3) = - 2.\]

\[Ответ:(6;1);( - 2; - 3).\]