Đáp án:
$\begin{array}{l}
a)\frac{x}{2} = \frac{y}{5} = \frac{{x + y}}{{2 + 5}} = \frac{{35}}{7} = 5\\
\Rightarrow \left\{ \begin{array}{l}
x = 5.2 = 10\\
y = 5.5 = 25
\end{array} \right.\\
Vậy\,x = 10;y = 25\\
b)\frac{{x + 2}}{{y + 10}} = \frac{1}{5};y - 3x = 2\\
\Rightarrow y = 3x + 2\\
\Rightarrow \frac{{x + 2}}{{3x + 2 + 10}} = \frac{1}{5}\\
\Rightarrow 5\left( {x + 2} \right) = 3x + 12\\
\Rightarrow 5x + 10 = 3x + 12\\
\Rightarrow 5x - 3x = 12 - 10\\
\Rightarrow 2x = 2\\
\Rightarrow x = 1\\
\Rightarrow y = 3x + 2 = 5\\
c)\frac{x}{4} = \frac{y}{5} = \frac{{2x}}{8} = \frac{{2x - y}}{{8 - 5}} = \frac{{15}}{3} = 5\\
\Rightarrow \left\{ \begin{array}{l}
x = 4.5 = 20\\
y = 5.5 = 25
\end{array} \right.\\
Vậy\,\left( {x;y} \right) = \left( {20;25} \right)
\end{array}$
