Решите систему уравнений: x=4-y; x^2+3xy=18.

Ответ:

\[\left\{ \begin{matrix} y = 4 - x\ \ \ \ \ \ \ \\ x^{2} + 3xy = 18 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = 4 - x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} + 3x(4 - x) = 18 \\ \end{matrix} \right.\ \text{\ \ \ \ }\]

\[\left\{ \begin{matrix} y = 4 - x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x^{2} + 12x - 3x^{2} - 18 = 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} y = 4 - x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ - 2x^{2} + 12x - 18 = 0 \\ \end{matrix} \right.\ \]

\[x² - 6x + 9 = 0\]

\[(x - 3)^{2} = 0\]

\[x = 3\]

\[\left\{ \begin{matrix} x = 3 \\ y = 1 \\ \end{matrix} \right.\ \]

\[Ответ:(3;1).\]