Bạn tham khảo!
$\dfrac{x}{2}$ $=$ $\dfrac{y}{3}$; $\dfrac{y}{2}$ $=$ $\dfrac{z}{3}$ và $3x$ $-$ $4y$ $+$ $9z$ $=$ $69$
$→$ $\dfrac{x}{2}$ $=$ $\dfrac{y}{3}$ $→$ $\dfrac{x}{2}$ $.$ $\dfrac{1}{2}$ $=$ $\dfrac{y}{3}$ $.$ $\dfrac{1}{2}$
$→$ $\dfrac{x}{4}$ $=$ $\dfrac{y}{6}$ (1)
$→$ $\dfrac{y}{2}$ $=$ $\dfrac{z}{3}$ $→$ $\dfrac{y}{2}$ $.$ $\dfrac{1}{3}$ $=$ $\dfrac{z}{3}$ $.$ $\dfrac{1}{3}$
$→$ $\dfrac{y}{6}$ $=$ $\dfrac{z}{9}$ (2)
Từ (1) và (2) $→$ $\dfrac{x}{4}$ $=$ $\dfrac{y}{6}$ $=$ $\dfrac{z}{9}$
$→$ $\dfrac{3x}{12}$ $=$ $\dfrac{4y}{24}$ $=$ $\dfrac{9z}{81}$

Áp dụng t/c dãy tỉ số = nhau ta có :
$\dfrac{3x}{12}$ $=$ $\dfrac{4y}{24}$ $=$ $\dfrac{9z}{81}$ $=$ $\dfrac{3x-4y+9z}{12-24+81}$ $=$ $\dfrac{69}{69}$ $=$ $1$
$→$ $\dfrac{3x}{12}$ $=$ $1$ $→$ $3x$ $=$ $12$ $.$ $1$ $=$ $12$ $→$ $x$ $=$ $12$ $:$ $3$ $=$ $4$
và $\dfrac{4y}{24}$ $=$ $1$ $→$ $4y$ $=$ $24$ $.$ $1$ $=$ $24$ $→$ $y$ $=$ $24$ $:$ $4$ $=$ $6$

và $\dfrac{9z}{81}$ $=$ $1$ → 9z = 81 . 1 = 81 → z = 81 : 9 = 9
$FbBinhne2k88$

$\dfrac{x}{2}=\dfrac{y}{3},\dfrac{y}{2}=\dfrac{z}{3}$

$→\dfrac{x}{4}=\dfrac{y}{6}=\dfrac{z}{9}$

$→\dfrac{3x}{12}=\dfrac{4y}{24}=\dfrac{9z}{81}$

Áp dụng tính chất dãy tỉ số bằng nhau:

$\dfrac{3x}{12}=\dfrac{4y}{24}=\dfrac{9z}{81}=\dfrac{3x-4y+9z}{12-24+81}=\dfrac{69}{69}=1$

$→\dfrac{x}{4}=1→x=4$

   $\dfrac{y}{6}=1→y=6$

   $\dfrac{z}{9}=1→z=9$

Vậy $(x;y;z)=(4;6;9)$