[tex]\displaystyle\bf\\\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=k\\\\x=2k\\y=3k\\z=5k\\\\2x+ y+3z=44\\\\2\cdot2k+3k+3\cdot5k=44\\\\4k+3k+15k=44\\\\22k=44\\\\k=\frac{44}{22}\\\\\boxed{\bf~k=2}\\\\x=2k=2\cdot2=4\\y=3k=3\cdot2=6\\z=5k=5\cdot2=10\\\\\boxed{\begin{cases}\bf~x=4\\\bf~y=6\\\bf~z=10\end{cases}}[/tex]
