18 If $|x|+x+5 y=2$ and $|y|-y+x=7$, find the value of $x+y+2009$.
18 Answer: (2012)
Suppose $y \geq 0$. From $|y|-y+x=7$ we have $x=7$ and from $|x|+x+5 y=2$ we have $y=-\frac{12}{5}0(\rightarrow \leftarrow)$. So $x>0$.
Hence the two equations become $-2 y+x=7$ and $2 x+5 y=2 \Rightarrow x=\frac{13}{3}, y=-\frac{4}{3}$.