4. Determine the integer numbers $x$ and $y$ for which:

$$
\|x-3|+| y-2 x\|=3
$$

Supliment, G.M., November 2013
## Solution:

$$
\begin{aligned}
& |x-3|+|y-2 x|=3 \\
& |x-3|,|y-2 x| \in \mathbb{N} \\
& |x-3| \in\{0,1,2,3\}
\end{aligned}
$$

Completion:

$(3,9) ;(3,3) ;(4,10) ;(4,6) ;(2,6) ;(2,2) ;(5,11) ;(5,9) ;(1,3) ;(1,1) ;(0,0) ;(6,12)$ $3 p$