Решите систему уравнений (2x+3y)/4+(3x-2y)/5=-1/20; (3x+4y)/2-(5x-y)/3=43/6.

Ответ:

\[\left\{ \begin{matrix} \frac{2x + 3y}{4} + \frac{3x - 2y}{5} = - \frac{1}{20}\ \ | \cdot 20 \\ \frac{3x + 4y}{2} - \frac{5x - y}{3} = \frac{43}{6}\ \ \ \ \ \ \ \ \ \ \ \ \ \ | \cdot 6 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 10x + 15y + 12x - 8y = - 1 \\ 9x + 12y - 10x + 2y = 43\ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 22x + 7y = - 1\ \ \ \ | \cdot 2 \\ - x + 14y = 43\ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 44x + 14y = - 2 \\ - x + 14y = 43\ \ \ \\ \end{matrix} \right.\ ( - )\]

\[45x = - 45\]

\[x = - 1.\]

\[14y = 43 + x = 43 - 1\]

\[14y = 42\]

\[y = 3.\]

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

\[Ответ:( - 1;3).\]