Đáp án:
$\begin{array}{l}
a)\dfrac{x}{6} = \dfrac{y}{8} = \dfrac{z}{5} = \dfrac{{x + y - z}}{{6 + 8 - 5}}\\
= \dfrac{{18}}{9} = 2\\
\Leftrightarrow x = 12,y = 16,z = 10\\
Vậy\,x = 12,y = 16,z = 10\\
b)\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4} = \dfrac{{5x}}{{10}} = \dfrac{{2y}}{6} = \dfrac{{3z}}{{12}}\\
= \dfrac{{5x + 2y - 3z}}{{10 + 6 - 12}} = \dfrac{{ - 20}}{4} = - 5\\
Vậy\,x = - 10,y = - 15,z = - 20\\
c)\dfrac{x}{3} = \dfrac{y}{2},\dfrac{y}{7} = \dfrac{z}{5}\\
\Leftrightarrow \dfrac{x}{{21}} = \dfrac{y}{{14}} = \dfrac{z}{{10}} = \dfrac{{4x}}{{84}} = \dfrac{{3z}}{{30}}\\
= \dfrac{{4x - y + 3z}}{{84 - 14 + 30}} = \dfrac{{200}}{{100}} = 2\\
\Leftrightarrow x = 42,y = 28,z = 20\\
Vậy\,x = 42,zy = 28,z = 20\\
d)7x = 9y = 21z\\
\Leftrightarrow \dfrac{{7x}}{{63}} = \dfrac{{9y}}{{63}} = \dfrac{{21z}}{{63}}\\
\Leftrightarrow \dfrac{x}{9} = \dfrac{y}{7} = \dfrac{z}{3} = \dfrac{{x - y + z}}{{9 - 7 + 3}}\\
= \dfrac{{ - 15}}{5} = - 3\\
\Leftrightarrow x = - 27,y = - 21,z = - 9\\
Vậy\,x = - 27,y = - 21,z = - 9\\
e)\dfrac{4}{5}x = \dfrac{5}{6}y = \dfrac{{10}}{{11}}z\\
\Leftrightarrow \dfrac{1}{{20}}.\dfrac{4}{5}x = \dfrac{1}{{20}}.\dfrac{5}{6}y = \dfrac{1}{{20}}.\dfrac{{10}}{{11}}z\\
\Leftrightarrow \dfrac{x}{{25}} = \dfrac{y}{{24}} = \dfrac{z}{{22}} = \dfrac{{x + y + z}}{{25 + 24 + 22}} = \dfrac{{710}}{{71}} = 10\\
\Leftrightarrow x = 250,y = 240,z = 220\\
Vậy\,x = 250,y = 240,z = 220
\end{array}$
