7. If the system of equations concerning $x$ and $y$ $\left\{\begin{array}{l}a x+b y=1, \\ x^{2}+y^{2}=10\end{array}\right.$ has solutions, and all solutions are integers, then the number of ordered pairs $(a, b)$ is $\qquad$
$=7.32$.
Since the integer solutions of $x^{2}+y^{2}=10$ are
$$
\begin{array}{l}
(1,3),(3,1),(1,-3),(-3,1), \\
(-1,3),(3,-1),(-1,-3),(-3,-1),
\end{array}
$$

Therefore, the number of lines connecting these eight points that do not pass through the origin is 24, and the number of tangents passing through these eight points is 8. Each line determines a unique ordered pair $(a, b)$. Hence, the number of ordered pairs $(a, b)$ is 32.