Giúp mình bài 3 nha cho 5 sao + hay nhất

Đáp án:

$\begin{array}{l}
a)\left\{ \begin{array}{l}
\dfrac{x}{6} = \dfrac{y}{4} \Leftrightarrow \dfrac{x}{{24}} = \dfrac{y}{{16}}\\
\dfrac{x}{8} = \dfrac{z}{{ - 3}} \Leftrightarrow \dfrac{x}{{24}} = \dfrac{z}{{ - 9}}
\end{array} \right.\\
 \Leftrightarrow \dfrac{x}{{24}} = \dfrac{y}{{16}} = \dfrac{z}{{ - 9}} = \dfrac{{x + y + z}}{{24 + 16 - 9}} = \dfrac{2}{{31}}\\
 \Leftrightarrow \left\{ \begin{array}{l}
x = 24.\dfrac{2}{{31}} = \dfrac{{48}}{{31}}\\
y = 16.\dfrac{2}{{31}} = \dfrac{{32}}{{31}}\\
z =  - 9.\dfrac{2}{{31}} = \dfrac{{ - 18}}{{31}}
\end{array} \right.\\
Vậy\,x = \dfrac{{48}}{{31}};y = \dfrac{{32}}{{31}};z =  - \dfrac{{18}}{{31}}\\
b)\left\{ \begin{array}{l}
\dfrac{x}{3} = \dfrac{y}{{10}} \Leftrightarrow \dfrac{x}{9} = \dfrac{y}{{30}}\\
\dfrac{y}{{15}} = \dfrac{z}{4} \Leftrightarrow \dfrac{y}{{30}} = \dfrac{z}{8}
\end{array} \right.\\
 \Leftrightarrow \dfrac{x}{9} = \dfrac{y}{{30}} = \dfrac{z}{8} = \dfrac{{3x}}{{27}} = \dfrac{{3x - y}}{{27 - 30}} = \dfrac{6}{{ - 3}} =  - 2\\
 \Leftrightarrow \left\{ \begin{array}{l}
x =  - 18\\
y =  - 60\\
z =  - 16
\end{array} \right.\\
c)x:y:z = 3:2:5\\
 \Leftrightarrow \dfrac{x}{3} = \dfrac{y}{2} = \dfrac{z}{5} = \dfrac{{2x}}{6} = \dfrac{{4y}}{8}\\
 = \dfrac{{z - 2x + 4y}}{{5 - 6 + 8}} = \dfrac{{14}}{7} = 2\\
 \Leftrightarrow \left\{ \begin{array}{l}
x = 6\\
y = 4\\
z = 10
\end{array} \right.\\
Vậy\,x = 6;y = 4;z = 10\\
d)3x = 4y = 2z\\
 \Leftrightarrow \dfrac{{3x}}{{12}} = \dfrac{{4y}}{{12}} = \dfrac{{2z}}{{12}}\\
 \Leftrightarrow \dfrac{x}{4} = \dfrac{y}{3} = \dfrac{z}{6} = \dfrac{{y - z}}{{3 - 6}} = \dfrac{6}{{ - 3}} =  - 2\\
 \Leftrightarrow \left\{ \begin{array}{l}
x =  - 8\\
y =  - 6\\
z =  - 12
\end{array} \right.\\
Vậy\,x =  - 8;y =  - 6;z =  - 12
\end{array}$