1994 AIME Problem 7

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?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.