Đáp án:
Áp dụng tính chất dãy tỉ số bằng nhau
$\begin{array}{l}
a)2x = 3y\\
\Leftrightarrow \dfrac{x}{3} = \dfrac{y}{2} = \dfrac{{x + y}}{{2 + 3}} = \dfrac{{10}}{5} = 2\\
\Leftrightarrow x = 6,y = 4\\
Vậy\,x = 6,y = 4\\
b)3x = 5y\\
\Leftrightarrow \dfrac{x}{5} = \dfrac{y}{3} = \dfrac{{x + y}}{{5 + 3}} = \dfrac{{40}}{8} = 5\\
\Leftrightarrow x = 25,y = 15\\
Vậy\,x = 25,y = 15\\
c)4x = 3y\\
\Leftrightarrow \dfrac{x}{3} = \dfrac{y}{4} = \dfrac{{x - y}}{{3 - 4}} = \dfrac{{11}}{{ - 1}} = - 11\\
\Leftrightarrow \left\{ \begin{array}{l}
x = - 11.3 = - 33\\
y = - 11.4 = - 44
\end{array} \right.\\
Vậy\,x = - 33;y = - 44\\
d) - 2x = 5y\\
\Leftrightarrow \dfrac{x}{5} = \dfrac{y}{{ - 2}} = \dfrac{{x + y}}{{5 - 2}} = \dfrac{{30}}{3} = 10\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 50\\
y = - 20
\end{array} \right.\\
Vậy\,x = 50;y = - 20\\
e)\dfrac{{2x}}{3} = \dfrac{{5y}}{4}\\
\Leftrightarrow \dfrac{{2x}}{{3.10}} = \dfrac{{5y}}{{4.10}}\\
\Leftrightarrow \dfrac{{2x}}{{30}} = \dfrac{y}{8} = \dfrac{{2x + y}}{{30 + 8}} = \dfrac{{76}}{{38}} = 2\\
\Leftrightarrow \left\{ \begin{array}{l}
x = \dfrac{{2.30}}{2} = 30\\
y = 2.8 = 16
\end{array} \right.\\
Vậy\,x = 30;y = 16\\
f)\dfrac{{3x}}{2} = \dfrac{{4y}}{7}\\
\Leftrightarrow \dfrac{{3x}}{{2.12}} = \dfrac{{4y}}{{7.12}}\\
\Leftrightarrow \dfrac{x}{8} = \dfrac{y}{{21}} = \dfrac{{5x}}{{40}} = \dfrac{{2y}}{{42}} = \dfrac{{5x - 2y}}{{40 - 42}} = \dfrac{{54}}{{ - 2}} = - 27\\
\Leftrightarrow \left\{ \begin{array}{l}
x = - 27.8 = - 216\\
y = - 27.21 = - 576
\end{array} \right.\\
Vậy\,x = - 216;y = - 576
\end{array}$
