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.