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

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

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

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

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

\[77x = 154\]

\[x = 154\ :77\]

\[x = 2.\]

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

\[7y = - 7\]

\[y = - 1.\]

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

\[Ответ:(2;\ - 1).\]