\(\left\{{}\begin{matrix}3x-y=5\\2x+my=3m-4\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}6x-2y=10\\6x+3my=9m-12\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3my+2y=9m-22\\6x-2y=10\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y\left(3m+2\right)=9m-22\\6x-2y=10\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=\dfrac{9m-22}{3m+2}\\6x-2.\dfrac{9m-22}{3m+2}=10\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=3-\dfrac{28}{3m+2}\\6x-\dfrac{18m-44}{3m+2}=10\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}y=3-\dfrac{28}{3m+2}\\6x-6+\dfrac{56}{3m+2}=10\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=3-\dfrac{28}{3m+2}\\6x+\dfrac{56}{3m+2}=16\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=3-\dfrac{28}{3m+2}\\6x=16-\dfrac{56}{3m+2}=\dfrac{48m-24}{3m+2}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y=3-\dfrac{28}{3m+2}\\x=\dfrac{8m-4}{3m+2}\end{matrix}\right.\)
2x + 3y = 7
\(\Rightarrow2.\dfrac{8m-4}{3m+2}+3.\left(3-\dfrac{28}{3m+2}\right)=7\)
\(\Rightarrow\dfrac{16m-8}{3m+2}+\dfrac{27m-66}{3m+2}=7\)
\(\Rightarrow\dfrac{16m-8+27m-66}{3m+2}=7\)
\(\Rightarrow\dfrac{43m-74}{3m+2}=7\)
=> 43m - 74 = 21m + 14
=> 43m - 74 - 21m - 14 = 0
=> 22m - 88 = 0
=> m = 4
