Đáp án:
\[x = 5;\,\,\,y = \dfrac{1}{4}\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\dfrac{{1 + 2y}}{{18}} = \dfrac{{1 + 4y}}{{24}} = \dfrac{{1 + 6y}}{{6x}}\\
\dfrac{{1 + 2y}}{{18}} = \dfrac{{1 + 4y}}{{24}}\\
\Leftrightarrow 24.\left( {1 + 2y} \right) = 18.\left( {1 + 4y} \right)\\
\Leftrightarrow 24 + 48y = 18 + 72y\\
\Leftrightarrow 24 - 18 = 72y - 48y\\
\Leftrightarrow 24y = 6\\
\Leftrightarrow y = \dfrac{1}{4}\\
\Rightarrow \dfrac{{1 + 2y}}{{18}} = \dfrac{{1 + 4y}}{{24}} = \dfrac{{1 + 6y}}{{6x}} = \dfrac{{1 + 4.\dfrac{1}{4}}}{{24}} = \dfrac{2}{{24}} = \dfrac{1}{{12}}\\
\dfrac{{1 + 6y}}{{6x}} = \dfrac{1}{{12}}\\
\Leftrightarrow 12.\left( {1 + 6y} \right) = 6x\\
\Leftrightarrow 12.\left( {1 + 6.\dfrac{1}{4}} \right) = 6x\\
\Leftrightarrow 12.\dfrac{5}{2} = 6x\\
\Leftrightarrow 30 = 6x\\
\Leftrightarrow x = 5
\end{array}\)
Vậy \(x = 5;\,\,\,y = \dfrac{1}{4}\)
