\(y\left(x+4\right)-12x\left(2-y\right)-13xy+24x=2004\)
\(\Leftrightarrow xy+4y-24x+12xy-13xy+24x=2004\)
\(\Leftrightarrow4y=2004\Leftrightarrow y=501\)
=> Biểu thức trên không phụ thuộc vào giá trị biến x
\(\Rightarrow\left\{{}\begin{matrix}x\in R\\y=501\end{matrix}\right.\)
\(xy+4y-24x+12xy-13xy+24x-2004=0\)
\(4y-2004=0\)
\(y=501\)
\(y\left(x+4\right)-12x\left(2-y\right)-13xy+24x=2004\\ \Leftrightarrow xy+4y-24x+12xy-13xy+24x=2004\\ \Leftrightarrow4y=2004\Leftrightarrow y=501\)
Thay vào bt ban đầu
\(\Leftrightarrow501\left(x+4\right)-12x\left(2-501\right)-13x\cdot501+24x=2004\\ \Leftrightarrow501x+2004-12x\cdot\left(-499\right)-6513x+24x=2004\\ \Leftrightarrow0x+2004=2004\\ \Leftrightarrow x=0\)
Vậy \(\left(x;y\right)=\left(0;501\right)\)
