# Circle and a line!

**Number Theory**Level 5

\[\begin{cases} ax+by=1 \\ x^2 + y^2 = 50 \end{cases} \]

For certain ordered pairs \((a,b)\) of real numbers, the system of equations above 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?