x+3y=2k+1 (1)
2x-y=k+3 (2)
(1)+(2)*3
7x=5k+10
x=(5k+10)/7
y=2x-k-3=(3k-1)/7
x>0,y>0
(5k+10)/7>0
(3k-1)/7>0
k>-2
k>1/3
所以k>1/3