\(\Leftrightarrow\left\{{}\begin{matrix}3x-2y=6\\5x-8y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}12x-8y=24\\5x-8y=3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}7x=21\\3x-2y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=\dfrac{3}{2}\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{x}{2}-\dfrac{y}{3}=1\\5x-8y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x-\dfrac{10}{3}y=10\\5x-8y=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}\dfrac{14}{3}y=7\\5x-8y=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{3}{2}\\5x-8.\dfrac{3}{2}=3\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{3}{2}\\x=3\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{x}{2}-\dfrac{y}{3}=1.\\5x-8y=3.\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x-2y=6.\\5x-8y=3.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}12x-8y=24.\\5x-8y=3.\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}7x=21.\\5x-8y=3.\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=3.\\y=\dfrac{3}{2}.\end{matrix}\right.\)
Vậy hệ phương trình có nghiệm duy nhất \(\left(x;y\right)=\left(3;\dfrac{3}{2}\right).\)
