Đáp án:
$\left( {x;y} \right) = \left( {5;\dfrac{3}{4}} \right)$
Giải thích các bước giải:
ĐK: $x\ne 0$
Ta có:
$\dfrac{{1 + 3y}}{{13}} = \dfrac{{1 + 5y}}{{19}} = \dfrac{{1 + 7y}}{{5x}}\left( 1 \right)$
$\begin{array}{l}
+ )\left( 1 \right) \Rightarrow \dfrac{{1 + 3y}}{{13}} = \dfrac{{1 + 5y}}{{19}}\\
\Leftrightarrow 19\left( {1 + 3y} \right) = 13\left( {1 + 5y} \right)\\
\Leftrightarrow 19 + 57y = 13 + 65y\\
\Leftrightarrow 8y = 6\\
\Leftrightarrow y = \dfrac{3}{4}\\
+ )\left( 1 \right) \Rightarrow \dfrac{{1 + 5y}}{{19}} = \dfrac{{1 + 7y}}{{5x}}\\
\Leftrightarrow \dfrac{{1 + 5.\dfrac{3}{4}}}{{19}} = \dfrac{{1 + 7.\dfrac{3}{4}}}{{5x}}\\
\Leftrightarrow \dfrac{1}{4} = \dfrac{5}{{4x}}\\
\Leftrightarrow x = 5
\end{array}$
Vậy $\left( {x;y} \right) = \left( {5;\dfrac{3}{4}} \right)$
