Решите систему уравнений: x^2-5xy+6y^2=0; 3x^2+2xy-y^2=15.

Ответ:

\[\left\{ \begin{matrix} x^{2} - 5xy + 6y^{2} = 0\ \ \\ 3x^{2} + 2xy - y^{2} = 15 \\ \end{matrix} \right.\ \]

\[x^{2} - 5xy + 6y^{2} = 0\]

\[D = 25y^{2} - 24y^{2} = y^{2}\]

\[x_{1} = \frac{5y - y}{2} = 2y;\ \ \ \ \]

\[x_{2} = \frac{5y + y}{2} = 3y\]