Đáp án: $\,\left( {x;y} \right) = \left\{ {\left( {10;\dfrac{{47}}{4}} \right);\left( { - 10; - 22} \right)} \right\}$
Giải thích các bước giải:
$\begin{array}{l}
\dfrac{{3x - 18}}{{16}} = \dfrac{{12}}{{x + 6}} = \dfrac{{y - 5}}{9}\\
Khi:\dfrac{{3x - 18}}{{16}} = \dfrac{{12}}{{x + 6}}\\
\Leftrightarrow \dfrac{{3.\left( {x - 6} \right)}}{{16}} = \dfrac{{12}}{{x + 6}}\\
\Leftrightarrow \dfrac{{x - 6}}{{16}} = \dfrac{4}{{x + 6}}\\
\Leftrightarrow \left( {x - 6} \right)\left( {x + 6} \right) = 16.4\\
\Leftrightarrow {x^2} + 6x - 6x - 36 = 64\\
\Leftrightarrow {x^2} - 36 = 64\\
\Leftrightarrow {x^2} = 100\\
\Leftrightarrow \left[ \begin{array}{l}
x = 10\\
x = - 10
\end{array} \right.\\
+ Khi:x = 10\\
Do\dfrac{{12}}{{x + 6}} = \dfrac{{y - 5}}{9}\\
\Leftrightarrow \dfrac{{12}}{{16}} = \dfrac{{y - 5}}{9}\\
\Leftrightarrow y - 5 = \dfrac{{12.9}}{{16}} = \dfrac{{27}}{4}\\
\Leftrightarrow y = \dfrac{{47}}{4}\\
+ Khi:x = - 10\\
Do\dfrac{{12}}{{x + 6}} = \dfrac{{y - 5}}{9}\\
\Leftrightarrow \dfrac{{12}}{{ - 10 + 6}} = \dfrac{{y - 5}}{9}\\
\Leftrightarrow \dfrac{{y - 5}}{9} = - 3\\
\Leftrightarrow y - 5 = - 27\\
\Leftrightarrow y = - 22\\
Vậy\,\left( {x;y} \right) = \left\{ {\left( {10;\dfrac{{47}}{4}} \right);\left( { - 10; - 22} \right)} \right\}
\end{array}$
