Решите систему уравнений (2x+3y)/2+(3x-2y)/7=43/14; (3x+2y)/2-(5x-y)/5=3/10.

Ответ:

\[\left\{ \begin{matrix} \frac{2x + 3y}{2} + \frac{3x - 2y}{7} = \frac{43}{14}\ \ \ | \cdot 14 \\ \frac{3x + 2y}{2} - \frac{5x - y}{5} = \frac{3}{10}\ \ \ \ \ \ | \cdot 10 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 14x + 21y + 6x - 4y = 43 \\ 15x + 10y - 10x + 2y = 3 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 20x + 17y = 43\ \ \ \ \\ 5x + 12y = 3\ \ | \cdot 4 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 20x + 17y = 43 \\ 20x + 48y = 12 \\ \end{matrix} \right.\ ( - )\]

\[- 31y = 31\]

\[y = - 1.\]

\[5x = 3 - 12y = 3 - 12 \cdot ( - 1) = 3 + 12\]

\[5x = 15\]

\[x = 3.\]

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

\[Ответ:(3;\ - 1).\]