Решите систему уравнений: y^2-xy+x=2; 5y+x=12.

Ответ:

\[\left\{ \begin{matrix} y^{2} - xy + x = 2 \\ 5y + x = 12\ \ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ \ } \right.\ \]

\[6y^{2} - 17y + 10 = 0\]

\[D = 289 - 240 = 49\]

\[y = \frac{17 + 7}{12} = 2,\]

\[y = \frac{17 - 7}{12} = \frac{5}{6}\]

\[\left\{ \begin{matrix} x = 2 \\ y = 2 \\ \end{matrix}\text{\ \ \ \ \ \ \ } \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} x = 7\frac{5}{6} \\ y = \frac{5}{6} \\ \end{matrix} \right.\ \]

\[Ответ:(2;2);\ \left( 7\frac{5}{6};\frac{5}{6} \right).\]