Đáp án:
$\begin{array}{l}
a)\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4} = \dfrac{{x + y - z}}{{2 + 3 - 4}} = 3\\
\Leftrightarrow x = 6,y = 9,z = 12\\
Vậy\,x = 6,y = 9,z = 12\\
b)\dfrac{x}{5} = \dfrac{y}{6} = \dfrac{z}{7}\\
\Leftrightarrow \dfrac{{2x}}{{10}} = \dfrac{y}{6} = \dfrac{z}{7} = \dfrac{{2x + y - z}}{{10 + 6 - 7}} = \dfrac{{27}}{9} = 3\\
\Leftrightarrow x = 15,y = 18,z = 21\\
Vậy\,x = 15,y - 18,z = 21\\
c)\dfrac{x}{3} = \dfrac{y}{5} = \dfrac{z}{6} = \dfrac{{x - z}}{{3 - 6}} = \dfrac{9}{{ - 3}} = - 3\\
\Leftrightarrow x = - 9,y = - 15,z = - 18\\
Vậy\,x = - 9,y = - 15,z = - 18\\
d)2x = 3y = 4z\\
\Leftrightarrow \dfrac{{2x}}{{12}} = \dfrac{{3y}}{{12}} = \dfrac{{4z}}{{12}}\\
\Leftrightarrow \dfrac{x}{6} = \dfrac{y}{4} = \dfrac{z}{3}\\
\Leftrightarrow \dfrac{x}{6} = \dfrac{{2y}}{8} = \dfrac{z}{3} = \dfrac{{x - 2y}}{{6 - 8}} = \dfrac{4}{{ - 2}} = - 2\\
\Leftrightarrow x = - 12,y = - 8,z = - 6\\
Vậy\,x = - 12,y = - 8,z = - 6
\end{array}$
