$\dfrac{x-1}{5}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$
$→\dfrac{2x-2}{10}=\dfrac{3y-6}{9}=\dfrac{z-3}{4}$
Áp dụng tính chất dãy tỉ số bằng nhau:
$\dfrac{2x-2}{10}=\dfrac{3y-6}{9}=\dfrac{z-3}{4}=\dfrac{2x-2+3y-6-z+3}{10+9-4}=\dfrac{2x+3y-z-5}{15}=\dfrac{50-5}{15}=\dfrac{45}{15}=3$
$→\begin{cases}\dfrac{x-1}{5}=3\\\dfrac{y-2}{3}=3\\\dfrac{z-3}{4}=3\end{cases}$
$→\begin{cases}x-1=15\\y-2=9\\z-3=12\end{cases}$
$→\begin{cases}x=16\\y=11\\z=15\end{cases}$
Vậy $(x;y;z)=(16;11;15)$
