\[\boxed{\text{419\ (419).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ \left\{ \begin{matrix} xy = 6\ \ \ \ \ \ \ \ \ \ \\ 2x - 3y = 6 \\ \end{matrix} \right.\ \text{\ \ }\left\{ \begin{matrix} y = \frac{6}{x}\text{\ \ \ \ \ \ \ \ \ \ \ \ } \\ 3y = 2x - 6 \\ \end{matrix} \right.\ \]
\[\left\{ \begin{matrix} y = \frac{6}{x}\text{\ \ \ \ \ \ \ \ \ \ \ } \\ y = \frac{2}{3}x - 2 \\ \end{matrix} \right.\ \]
\[(4,8;1,2);\ \ ( - 1,9;\ - 3,2).\]
\[\textbf{б)}\ \left\{ \begin{matrix} (x - 3)^{2} + (y - 4)^{2} = 4 \\ y - x^{2} = 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\ \left\{ \begin{matrix} (x - 3)^{2} + (y - 4)^{2} = 4 \\ y = x^{2}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \]
\[(x - 3)^{2} + (y - 4)^{2} = 4\]
\[окружность\ с\ центром\ (3;4)\ и\]
\[\ радиусом\ равным\ 2.\]
\[(1,6;2,5);\ \ \ (2,4;5,8).\]