Lời giải: \(\begin{aligned} &\text { Ta có }\left\{\begin{array}{l} \frac{2 x+1}{3}-\frac{y+1}{4}=\frac{4 x-2 y+2}{5} \\ \frac{2 x-3}{4}-\frac{y-4}{3}=-2 x+2 y-2 \end{array}\right.\\ &\Leftrightarrow\left\{\begin{array}{l} 40 x+20-15 y-15=48 x-24 y+24 \\ 6 x-9-4 y+16=-24 x+24 y-24 \end{array} \Leftrightarrow\left\{\begin{array}{l} 8 x-9 y=-19 \\ 30 x-28 y=-31 \end{array}\right.\right.\\ &\Leftrightarrow\left\{\begin{array}{l} 120 x-135 y=-285 \\ 120 x-112 y=-124 \end{array} \Leftrightarrow\left\{\begin{array}{l} x=\frac{11}{2} \\ y=7 \end{array}\right.\right.\\ &\text { Thay } x=\frac{11}{2} ; y=7 \text { vào phương trình } 6 m x-5 y=2 m-66 \text { ta được } \end{aligned}\)
\(6 m \cdot \frac{11}{2}-5.7=2 m-66 \Leftrightarrow 31 m=-31 \Leftrightarrow m=-1\)
