Решите систему уравнений (2x+7y)/4+(3x-2y)/3=2/3; (3x+2y)/2-(4x-6y)/7=39/14.

Ответ:

\[\left\{ \begin{matrix} \frac{2x + 7y}{4} + \frac{3x - 2y}{3} = \frac{2}{3}\ \ \ \ | \cdot 12 \\ \frac{3x + 2y}{2} - \frac{4x - 6y}{7} = \frac{39}{14}\ \ | \cdot 14 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 6x + 21y + 12x - 8y = 8\ \ \ \ \\ 21x + 14y - 8x + 12y = 39 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 18x + 13y = 8\ \ \ | \cdot 2 \\ 13x + 26y = 39\ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 36x + 26y = 16 \\ 13x + 26y = 36 \\ \end{matrix} \right.\ ( - )\]

\[23x = - 23\]

\[x = - 1.\]

\[13y = 8 - 18x = 8 + 18\]

\[13y = 26\]

\[y = 2.\]

\[\left\{ \begin{matrix} x = - 1 \\ y = 2\ \ \ \\ \end{matrix} \right.\ \]

\[Ответ:( - 1;2).\]