Đáp án:

Áp dụng tính chất dãy tỉ số bằng nhau

$\begin{array}{l}
1)\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{5} = \dfrac{{x + y + z}}{{2 + 3 + 5}} = \dfrac{{ - 90}}{{10}} =  - 9\\
 \Leftrightarrow \left\{ \begin{array}{l}
x =  - 18\\
y =  - 27\\
z =  - 45
\end{array} \right.\\
Vậy\,x =  - 18;y =  - 27;z =  - 45\\
2)2x = 3y = 5z\\
 \Leftrightarrow \dfrac{{2x}}{{30}} = \dfrac{{3y}}{{30}} = \dfrac{{5z}}{{30}}\\
 \Leftrightarrow \dfrac{x}{{15}} = \dfrac{y}{{10}} = \dfrac{z}{6} = \dfrac{{x - y + z}}{{15 - 10 + 6}} = \dfrac{{ - 33}}{{11}} =  - 3\\
 \Leftrightarrow \left\{ \begin{array}{l}
x =  - 45\\
y =  - 30\\
z =  - 18
\end{array} \right.\\
Vậy\,x =  - 45;y =  - 30;z =  - 18\\
4)\dfrac{{x - 1}}{2} = \dfrac{{y + 3}}{4} = \dfrac{{z - 5}}{6}\\
 \Leftrightarrow \dfrac{{x - 1}}{1} = \dfrac{{y + 3}}{2} = \dfrac{{z - 5}}{3}\\
 = \dfrac{{3x - 3}}{3} = \dfrac{{4y + 12}}{8} = \dfrac{{5z - 25}}{{15}}\\
 = \dfrac{{5z - 25 - 3x + 3 - 4y - 12}}{{15 - 3 - 8}}\\
 = \dfrac{{50 - 25 + 3 - 12}}{4} = \dfrac{{16}}{4} = 4\\
 \Leftrightarrow \left\{ \begin{array}{l}
x - 1 = 4\\
y + 3 = 8\\
z - 5 = 12
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 5\\
y = 5\\
z = 17
\end{array} \right.\\
Vậy\,x = y = 5;z = 17\\
2)2a = 3b;5b = 7c\\
 \Leftrightarrow \left\{ \begin{array}{l}
\dfrac{a}{3} = \dfrac{b}{2} \Leftrightarrow \dfrac{a}{{21}} = \dfrac{b}{{14}}\\
\dfrac{b}{7} = \dfrac{c}{5} \Leftrightarrow \dfrac{b}{{14}} = \dfrac{c}{{10}}
\end{array} \right.\\
 \Leftrightarrow \dfrac{a}{{21}} = \dfrac{b}{{14}} = \dfrac{c}{{10}}\\
 = \dfrac{{3a}}{{63}} = \dfrac{{7b}}{{98}} = \dfrac{{5c}}{{50}}\\
 = \dfrac{{3a + 5c - 7b}}{{63 + 50 - 98}} = \dfrac{{30}}{{15}} = 2\\
 \Leftrightarrow \left\{ \begin{array}{l}
a = 42\\
b = 28\\
c = 20
\end{array} \right.\\
Vậy\,a = 42;b = 28;c = 20\\
c)x:y:z = 3:8:5\\
 \Leftrightarrow \dfrac{x}{3} = \dfrac{y}{8} = \dfrac{z}{5}\\
 = \dfrac{{3x}}{9} = \dfrac{{2z}}{{10}} = \dfrac{{3x + y - 2z}}{{9 + 8 - 10}} = \dfrac{{14}}{7} = 2\\
 \Leftrightarrow \left\{ \begin{array}{l}
x = 6\\
y = 16\\
z = 10
\end{array} \right.\\
7)\dfrac{x}{1} = \dfrac{y}{2} = \dfrac{z}{3}\\
 = \dfrac{{4x}}{4} = \dfrac{{3y}}{6} = \dfrac{{2z}}{6}\\
 = \dfrac{{4x - 3y + 2z}}{{4 - 6 + 6}} = \dfrac{{36}}{4} = 9\\
 \Leftrightarrow \left\{ \begin{array}{l}
x = 9\\
y = 18\\
z = 27
\end{array} \right.\\
Vậy\,x = 9;y = 18;z = 27
\end{array}$