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)