Đáp án:

$\begin{array}{l}
a)3x = 4y\\
 \Leftrightarrow \dfrac{x}{4} = \dfrac{y}{3} = \dfrac{{y - x}}{{3 - 4}} = \dfrac{5}{{ - 1}} =  - 5\\
 \Leftrightarrow x =  - 20,y =  - 15\\
Vậy\,x =  - 20,y =  - 15\\
a)2x = 5y\\
 \Leftrightarrow \dfrac{x}{5} = \dfrac{y}{2} = \dfrac{{y - x}}{{5 - 2}} = \dfrac{{12}}{3} = 4\\
 \Leftrightarrow x = 20,y = 8\\
Vậy\,x = 20,y = 8\\
a)2x = 3y\\
 \Leftrightarrow \dfrac{x}{3} = \dfrac{y}{2} = \dfrac{{x + y}}{{3 + 2}} = \dfrac{{90}}{5} = 18\\
 \Leftrightarrow x = 54,y = 36\\
Vậy\,x = 54,y = 36\\
a)7x = 3y\\
 \Leftrightarrow \dfrac{x}{3} = \dfrac{y}{7} = \dfrac{{x - y}}{{3 - 7}} = \dfrac{{16}}{{ - 4}} =  - 4\\
 \Leftrightarrow x =  - 12,y =  - 28\\
Vậy\,x =  - 12,y =  - 28\\
a)8x = 5y\\
 \Leftrightarrow \dfrac{x}{5} = \dfrac{y}{8} = \dfrac{{2x}}{{10}} = \dfrac{{y - 2x}}{{8 - 10}} = \dfrac{{ - 10}}{{ - 2}} = 5\\
 \Leftrightarrow x = 25,y = 40\\
Vậy\,x = 25,y = 40\\
b)\dfrac{5}{2} = \dfrac{y}{x}\\
 \Leftrightarrow \dfrac{x}{2} = \dfrac{y}{5} = \dfrac{{x + y}}{{2 + 5}} = \dfrac{{ - 21}}{7} =  - 3\\
 \Leftrightarrow x =  - 6,y =  - 15\\
Vậy\,x =  - 6,y =  - 15\\
b)\dfrac{7}{5} = \dfrac{y}{x}\\
 \Leftrightarrow \dfrac{x}{5} = \dfrac{y}{7} = \dfrac{{x + y}}{{5 + 7}} = \dfrac{{36}}{{12}} = 3\\
 \Leftrightarrow x = 15,y = 21\\
Vậy\,x = 15,y = 21\\
b)\dfrac{x}{y} = \dfrac{2}{{ - 5}}\\
 \Leftrightarrow \dfrac{x}{2} = \dfrac{y}{{ - 5}} = \dfrac{{x - y}}{{2 - \left( { - 5} \right)}} = \dfrac{{ - 7}}{7} =  - 1\\
 \Leftrightarrow x =  - 2,y = 5\\
Vậy\,x =  - 2,y = 5\\
b)\dfrac{x}{y} = \dfrac{9}{{10}}\\
 \Leftrightarrow \dfrac{x}{9} = \dfrac{y}{{10}} = \dfrac{{y - x}}{{10 - 9}} = \dfrac{{120}}{1} = 120\\
 \Leftrightarrow x = 1080,y = 1200\\
Vậy\,x = 1080,y = 1200\\
b)\dfrac{x}{y} = \dfrac{3}{4}\\
 \Leftrightarrow \dfrac{x}{3} = \dfrac{y}{4} = \dfrac{{3x}}{9} = \dfrac{{5y}}{{20}} = \dfrac{{ - 3x + 5y}}{{ - 9 + 20}} = \dfrac{{33}}{{11}} = 3\\
 \Leftrightarrow x = 9,y = 12\\
Vậy\,x = 9,y = 12
\end{array}$