`{x-3}/2={y+1}/3=z/4`
`⇒{x-3}/2={2y+2}/6=z/4`
`⇒{x-3}/2={2y+2}/6=z/4={x-3+2y+2-z}/{2+6-4}` `(DTBN)`
`⇒{x-3}/2={2y+2}/6=z/4={(x+2y-z)-3+2}/{2+6-4}={5-3+2}/{2+6-4}=4/4`
`⇒{x-3}/2={y+1}/3=z/4=1`
$⇒\begin{cases}x-3=2\\y+1=3\\z=4\end{cases}$
$⇒\begin{cases}x=5\\y=2\\z=4\end{cases}$