Решите систему уравнений (2x+3y)/4+(3x-4y)/3=43/12; (3x+4y)/2-(5x-4y)/5=-9/5.

\[\left\{ \begin{matrix} \frac{2x + 3y}{4} + \frac{3x - 4y}{3} = \frac{43}{12}\ \ \ | \cdot 12 \\ \frac{3x + 4y}{2} - \frac{5x - 4y}{5} = - \frac{9}{5}\ \ \ \ | \cdot 10 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 6x + 9y + 12x - 16y = 43\ \ \ \ \ \ \\ 15x + 20y - 10x + 8y = - 18 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 18x - 7y = 43\ \ | \cdot 4 \\ 5x + 28y = - 18\ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 72x - 28y = 172 \\ 5x + 28y = - 18\ \\ \end{matrix} \right.\ ( + )\]

\[77x = 154\]

\[x = 154\ :77\]

\[x = 2.\]

\[7y = 18x - 43 = 18 \cdot 2 - 43 = 36 - 43\]

\[7y = - 7\]

\[y = - 1.\]

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

\[Ответ:(2;\ - 1).\]