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 \left\{ \begin{array}{l}
x = 12\\
y = 16\\
z = 10
\end{array} \right.\\
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\\
\Leftrightarrow \left\{ \begin{array}{l}
x = - 5.2 = - 10\\
y = - 5.3 = - 15\\
z = - 5.4 = - 20
\end{array} \right.\\
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{y}{{14}} = \dfrac{z}{{10}}\\
\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 \left\{ \begin{array}{l}
x = 2.21 = 42\\
y = 2.14 = 28\\
z = 2.10 = 20
\end{array} \right.\\
Vậy\,x = 42;y = 28;z = 20\\
d)5x = 2y \Leftrightarrow \dfrac{x}{2} = \dfrac{y}{5} \Leftrightarrow \dfrac{x}{8} = \dfrac{y}{{20}}\\
3y = 4z \Leftrightarrow \dfrac{y}{4} = \dfrac{z}{3} \Leftrightarrow \dfrac{y}{{20}} = \dfrac{z}{{15}}\\
\Leftrightarrow \dfrac{x}{8} = \dfrac{y}{{20}} = \dfrac{z}{{15}}\\
= \dfrac{{4x}}{{32}} = \dfrac{{3z}}{{45}}\\
= \dfrac{{4x - y + 3z}}{{32 - 20 + 45}} = \dfrac{{200}}{{57}}\\
\Leftrightarrow \left\{ \begin{array}{l}
x = \dfrac{{200}}{{57}}.8 = \dfrac{{1600}}{{57}}\\
y = \dfrac{{200}}{{57}}.20 = \dfrac{{4000}}{{57}}\\
z = \dfrac{{200}}{{57}}.15 = \dfrac{{1000}}{19}
\end{array} \right.\\
e)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 \left\{ \begin{array}{l}
x = - 3.9 = - 27\\
y = - 3.7 = - 21\\
z = - 3.3 = - 9
\end{array} \right.\\
Vậy\,x = - 27;y = - 21;z = - 9\\
f)\dfrac{4}{5}x = \dfrac{5}{6}y = \dfrac{{10}}{{11}}z\\
\Leftrightarrow \dfrac{{4x}}{{5.20}} = \dfrac{{5y}}{{6.20}} = \dfrac{{10z}}{{11.20}}\\
\Leftrightarrow \dfrac{x}{{25}} = \dfrac{y}{{24}} = \dfrac{z}{{22}} = \dfrac{{x + y + z}}{{25 + 24 + 22}} = \dfrac{{710}}{{71}} = 10\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 250\\
y = 240\\
z = 220
\end{array} \right.\\
Vậy\,x = 250;y = 240;z = 220
\end{array}$
