2x+y=k+ 1 (2)
( 1)×2-(2)
3y=2k-2-k- 1=k-3
y=(k-3)/3
x = k- 1-2y = k- 1-2(k-3)/3
x = k- 1-2(k-3)/3 & gt; 0
3(k- 1)>2 (k-3)
3k-3 & gt; 2k-6
k & gt-3
y =(k-3)/3 & lt; 0
k-3 & lt; 0
K< three
-3 & lt; K< three
K is an integer.
So k=-2,-1, 0, 1, 2.