Question 7
For certain ordered pairs $(a,b)$ of real numbers, the system of equations $$
\begin{aligned}ax+by&=1,\\x^2+y^2&=50\end{aligned}
$$ 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?
\begin{aligned}ax+by&=1,\\x^2+y^2&=50\end{aligned}
$$ 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?