Đáp án:
\(\left\{ \begin{array}{l}
x = 5\\
y = \frac{1}{4}
\end{array} \right.\)
Giải thích các bước giải:
\[\begin{array}{l}
\frac{{1 + 2y}}{{18}} = \frac{{1 + 4y}}{{24}} = \frac{{1 + 6y}}{{6x}}\\
Ta\,\,\,co:\\
\frac{{1 + 2y}}{{18}} = \frac{{1 + 4y}}{{24}}\\
\Leftrightarrow 24\left( {1 + 2y} \right) = 18\left( {1 + 4y} \right)\\
\Leftrightarrow 24 + 48y = 18 + 72y\\
\Leftrightarrow 24 - 18 = 72y - 48y\\
\Leftrightarrow 6 = 24y\\
\Leftrightarrow y = \frac{1}{4}\\
\Rightarrow \frac{{1 + 4y}}{{24}} = \frac{{1 + 6y}}{{6x}}\\
\Leftrightarrow \frac{{1 + 4.\frac{1}{4}}}{{24}} = \frac{{1 + 6.\frac{1}{4}}}{{6x}}\\
\Leftrightarrow \frac{2}{{24}} = \frac{5}{{12x}}\\
\Leftrightarrow 24x = 120\\
\Leftrightarrow x = 5.\\
Vay\,\,\left\{ \begin{array}{l}
x = 5\\
y = \frac{1}{4}
\end{array} \right..
\end{array}\]
