\(a,m=1\Leftrightarrow\left\{{}\begin{matrix}x-y=1\\\dfrac{x}{2}-\dfrac{y}{3}=334\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1+y\\\dfrac{1+y}{2}-\dfrac{y}{3}=334\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=1+y\\3y+3-2y=2004\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1+y\\y=2001\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2002\\y=2001\end{matrix}\right.\)
\(b,\left\{{}\begin{matrix}mx-y=1\\\dfrac{x}{2}-\dfrac{y}{3}=334\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}mx-y=1\\3x-2y=2004\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}mx-y=1\\y=\dfrac{3x-2004}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}mx-\dfrac{3x-2004}{2}=1\\y=\dfrac{3x-2004}{2}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}2mx-3x=-2002\\y=\dfrac{3x-2004}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\left(2m-3\right)=-2002\\y=\dfrac{3x-2004}{2}\end{matrix}\right.\)
Để hpt vô nghiệm thì \(x\left(2m-3\right)=-2002\) vô nghiệm
\(\Leftrightarrow2m-3=0\Leftrightarrow m=\dfrac{3}{2}\)
