Putnam 1975 B1

Consider the additive group $\mathbb{Z}^{2}$ . Let $H$ be the smallest subgroup containing $(3,8), (4,-1)$ and $(5,4)$ . Let $H_{xy}$ be the smallest subgroup containing $(0,x)$ and $(1,y)$ . Find some pair $(x,y)$ with $x>0$ such that $H=H_{xy}$ .