For certain ordered pairs $$(a,b)\,$$ of real numbers, the system of equations $$ax+by=1\,$$ $$x^2+y^2=50\,$$ has at least one solution, and each solution is an ordered pair $$(x,y)\,$$ of integers. How many such ordered pairs $$(a,b)\,$$ are there?

(第十二届AIME1994 第7题)