\(\left\{{}\begin{matrix}\dfrac{x-5y}{4}-\dfrac{3x-2y}{3}=-\dfrac{25}{24}\\\dfrac{5x+3y}{8}+\dfrac{x-6y}{5}=\dfrac{33}{80}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3\left(x-5y\right)-4\left(3x-2y\right)}{12}=-\dfrac{25}{24}\\\dfrac{5\left(5x+3y\right)+8\left(x-6y\right)}{40}=\dfrac{33}{80}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3x-15y-12x+8y}{12}=-\dfrac{25}{24}\\\dfrac{25x+15y+8x-48y}{40}=\dfrac{33}{80}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2\left(-9x-7y\right)}{24}=-\dfrac{25}{24}\\\dfrac{2\left(33x-33y\right)}{80}=\dfrac{33}{80}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}18x+14y=25\\2x-2y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}18x+14y=25\\14x-14y=7\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}32x=32\\2x-2y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\2\cdot1-2y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=\dfrac{1}{2}\end{matrix}\right.\)
