x+Y=a ① 5x+3y=31②
(2)-(1)*3
2x=31-3a
x=(31-3a)/2
y=a-x=(5a-31)/2
x>0,y>0
x=(31-3a)/2>0
31-3a>0
a<31/3
y=(5a-31)/2>0
5a-31>0
a>31/5
所以31/5所以a=7,8,9,10