{(x,y)|x+2y=7 xy为正整数,

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{(x,y)|x+2y=7xy为正整数,{(x,y)|x+2y=7xy为正整数,{(x,y)|x+2y=7xy为正整数,2y=7-x>0x(1,3)(3,2)(5,1)xy为正整数,,则x 

{(x,y)|x+2y=7 xy为正整数,
{(x,y)|x+2y=7 xy为正整数,

{(x,y)|x+2y=7 xy为正整数,
2y=7-x>0
x

(1,3) (3,2) (5,1)

xy为正整数,,则x ,y 为同号,因直线x+2y=7 不经过第三象限,因此,符合条件的x 、 y均为正整数。于是,

0 < x  ≤7  ,0 < y <4

则 (1,3),(3,2)(5,1)满足条件