Đáp án: $\left( {x;y} \right) = \left\{ {\left( { - 15,84;7,96} \right);\left( { - 0,085;0,084} \right)} \right\}$
Giải thích các bước giải:
$\begin{array}{l}
Dkxd:x;y\# 0\\
\left\{ \begin{array}{l}
\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{{16}}\\
3x + 6y = \dfrac{1}{4} \Leftrightarrow x = \dfrac{1}{{12}} - 2y
\end{array} \right.\\
\Leftrightarrow \dfrac{1}{{\dfrac{1}{{12}} - 2y}} + \dfrac{1}{y} = \dfrac{1}{{16}}\\
\Leftrightarrow \dfrac{{12}}{{1 - 24y}} + \dfrac{1}{y} = \dfrac{1}{{16}}\\
\Leftrightarrow \dfrac{{12y + 1 - 24y}}{{\left( {1 - 24y} \right).y}} = \dfrac{1}{{16}}\\
\Leftrightarrow y - 24{y^2} = 16.\left( {1 - 12y} \right)\\
\Leftrightarrow y - 24{y^2} = 16 - 192y\\
\Leftrightarrow 24{y^2} - 193y + 16 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
y = 7,96 \Leftrightarrow x = - 15,84\\
y = 0,084 \Leftrightarrow x = - 0,085
\end{array} \right.\\
Vay\,\left( {x;y} \right) = \left\{ {\left( { - 15,84;7,96} \right);\left( { - 0,085;0,084} \right)} \right\}
\end{array}$
