Đáp án:
Áp dụng tính chất dãy tỉ số bằng nhau
$\begin{array}{l}
a)\dfrac{x}{2} = \dfrac{y}{4} = \dfrac{z}{6} = \dfrac{{x - y + z}}{{2 - 4 + 6}} = \dfrac{{ - 16}}{4} = - 4\\
\Leftrightarrow \left\{ \begin{array}{l}
x = - 4.2 = - 8\\
y = - 4.4 = - 16\\
z = - 4.6 = - 24
\end{array} \right.\\
Vay\,x = - 8;y = - 16;z = - 24\\
b)2x = 3y = 5z\\
\Leftrightarrow \dfrac{{2x}}{{30}} = \dfrac{{3y}}{{30}} = \dfrac{{5z}}{{30}}\\
= \dfrac{x}{{15}} = \dfrac{y}{{10}} = \dfrac{z}{6} = \dfrac{{x + y - z}}{{15 + 10 - 6}} = \dfrac{{45}}{{19}}\\
\Leftrightarrow \left\{ \begin{array}{l}
x = \dfrac{{45}}{{19}}.15 = \dfrac{{675}}{{19}}\\
y = \dfrac{{45}}{{19}}.10 = \dfrac{{450}}{{19}}\\
z = \dfrac{{45}}{{19}}.6 = \dfrac{{270}}{{19}}
\end{array} \right.\\
c)\dfrac{x}{y} = \dfrac{2}{3} \Leftrightarrow \dfrac{x}{2} = \dfrac{y}{3} \Leftrightarrow \dfrac{x}{8} = \dfrac{y}{{12}}\\
\dfrac{y}{z} = \dfrac{4}{5} \Leftrightarrow \dfrac{y}{4} = \dfrac{z}{5} \Leftrightarrow \dfrac{y}{{12}} = \dfrac{z}{{15}}\\
\Leftrightarrow \dfrac{x}{8} = \dfrac{y}{{12}} = \dfrac{z}{{15}} = \dfrac{{x - y - z}}{{8 - 12 - 15}} = \dfrac{{38}}{{ - 19}} = - 2\\
\Leftrightarrow \left\{ \begin{array}{l}
x = - 16\\
y = - 24\\
z = - 30
\end{array} \right.\\
d)\dfrac{x}{y} = \dfrac{3}{4} \Leftrightarrow \dfrac{x}{3} = \dfrac{y}{4} \Leftrightarrow \dfrac{x}{{15}} = \dfrac{y}{{20}}\\
\dfrac{y}{z} = \dfrac{5}{7} \Leftrightarrow \dfrac{y}{5} = \dfrac{z}{7} \Leftrightarrow \dfrac{y}{{20}} = \dfrac{z}{{28}}\\
\Leftrightarrow \dfrac{x}{{15}} = \dfrac{y}{{20}} = \dfrac{z}{{28}} = \dfrac{{2x}}{{30}}\\
= \dfrac{{2x + y - z}}{{30 + 20 - 28}} = \dfrac{{ - 44}}{{22}} = - 2\\
\Leftrightarrow \left\{ \begin{array}{l}
x = - 30\\
y = - 40\\
z = - 56
\end{array} \right.
\end{array}$
