Lời giải:
Xét 2 trường hợp sau:
TH1: \(xy\geq 0\Rightarrow |xy|=xy\)
HPT \(\Leftrightarrow \left\{\begin{matrix} 17x+2y=2011xy(1)\\ x-2y=3xy(2)\end{matrix}\right.\)
\((1)+(2)\Rightarrow 18x=2014xy\Leftrightarrow x(18-2014y)=0\)
\(\Leftrightarrow \left[\begin{matrix} x=0\\ y=\frac{9}{1007}\end{matrix}\right.\)
Nếu \(x=0\Rightarrow -2y=0\Leftrightarrow y=0\) (t/m)
Nếu \(y=\frac{9}{1007}\Rightarrow x-\frac{18}{1007}=\frac{27x}{1007}\Leftrightarrow x=\frac{9}{490}\) (t/m)
TH2: \(xy\leq 0\Rightarrow |xy|=-xy\)
HPT \(\Leftrightarrow \left\{\begin{matrix} 17x+2y=-2011xy\\ x-2y=3xy\end{matrix}\right.\)
\(\Rightarrow 18x=-2011xy+3xy=-2008xy\)
\(\Leftrightarrow x(18+2008y)=0\)
Nếu \(x=0\Rightarrow -2y=0\Rightarrow y=0\) (t/m)
Nếu \(y=-\frac{9}{1004}\Rightarrow x+\frac{18}{1004}=\frac{-27x}{1004}\Leftrightarrow x=-\frac{18}{1031}\) (không t/m)
Vậy \((x,y)=(0,0); (\frac{9}{490}, \frac{9}{1007})\)
