Ta có: \(\left\{{}\begin{matrix}6\left(x+y\right)=8+2x-3y\\5\left(y-x\right)=5+3x+2y\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}6x+6y=8+2x-3y\\5y-5x=5+3x+2y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x-2x+6y+3y=8\\5y-5x-3x-2y=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4x+9y=8\\-8x+3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}8x+18y=16\\-8x+3y=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}21y=21\\4x+9y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\4x+9=8\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=1\\4x=8-9=-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{4}\\y=1\end{matrix}\right.\)
Vậy: Hệ phương trình có nghiệm duy nhất là \(\left\{{}\begin{matrix}x=-\dfrac{1}{4}\\y=1\end{matrix}\right.\)