Ta có:
$\dfrac{3x}{2}=\dfrac{4y}{5}=\dfrac{6z}{7}$
$→\dfrac{x}{\dfrac{2}{3}}=\dfrac{y}{\dfrac{5}{4}}=\dfrac{2z}{\dfrac{7}{3}}$
Áp dụng tính chất dãy tỉ số bằng nhau, ta có:
$\dfrac{x}{\dfrac{2}{3}}=\dfrac{y}{\dfrac{5}{4}}=\dfrac{2z}{\dfrac{7}{3}}=\dfrac{x-y-2z}{\dfrac{2}{3}-\dfrac{5}{4}-\dfrac{7}{3}}=\dfrac{-45}{-\dfrac{35}{12}}=\dfrac{108}{7}$
Tìm được:
$+)\dfrac{x}{\dfrac{2}{3}}=\dfrac{108}{7}→x=\dfrac{108}{7}.\dfrac{2}{3}=\dfrac{72}{7}$
$+)\dfrac{y}{\dfrac{5}{4}}=\dfrac{108}{7}→y=\dfrac{108}{7}.\dfrac{5}{4}=\dfrac{135}{7}$
$+)\dfrac{2z}{\dfrac{7}{3}}=\dfrac{108}{7}→2z=\dfrac{108}{7}.\dfrac{7}{3}=36→z=36:2=18$
Vậy `(x;y;z)=(72/7;135/7;18)`
