Đáp án:
$\begin{array}{l}
\frac{{2x}}{3} - \frac{2}{y} = \frac{1}{3}\\
\Rightarrow \frac{{2x}}{3} - \frac{1}{3} = \frac{2}{y}\\
\Rightarrow \frac{{2x - 1}}{3} = \frac{2}{y}\\
\Rightarrow \left( {2x - 1} \right).y = 3.2 = 6
\end{array}$
Do 2x-1 là 1 số lẻ nên ta có các giá trị là:
$\begin{array}{l}
\left[ \begin{array}{l}
\left\{ \begin{array}{l}
2x - 1 = - 1\\
y = - 6
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 0\\
y = - 6
\end{array} \right.\\
\left\{ \begin{array}{l}
2x - 1 = - 3\\
y = - 2
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = - 1\\
y = - 2
\end{array} \right.\\
\left\{ \begin{array}{l}
2x - 1 = 1\\
y = 6
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 1\\
y = 6
\end{array} \right.\\
\left\{ \begin{array}{l}
2x - 1 = 3\\
y = 2
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 2\\
y = 2
\end{array} \right.
\end{array} \right.\\
Vay\,\left( {x;y} \right) = \left\{ {\left( {0; - 6} \right);\left( { - 1; - 2} \right);\left( {1;6} \right);\left( {2;2} \right)} \right\}
\end{array}$
