$2x=3y→\dfrac{x}{3}=\dfrac{y}{2}$
$3y=5z→\dfrac{z}{3}=\dfrac{y}{5}$
$→\dfrac{x}{15}=\dfrac{y}{10}=\dfrac{z}{6}$
$→\dfrac{x}{15}=\dfrac{2y}{20}=\dfrac{3x}{18}$
Áp dụng tính chất dãy tỉ số bằng nhau:
$\dfrac{x}{15}=\dfrac{2y}{20}=\dfrac{3x}{18}=\dfrac{x-2y+3z}{15-20+18}=\dfrac{39}{13}=3$
$→\dfrac{x}{15}=3→x=3.15=45$
$→\dfrac{y}{10}=3→y=3.10=30$
$→\dfrac{z}{6}=3→z=3.6=18$
Vậy $(x;y;z)=(45;30;18)$
