30.3. The graphs of $x^{2}+y=12$ and $x+y=12$ intersect at two points. What is the distance between these points?
30.3. $\sqrt{2}$
Solving the following system of equations using the elimination method:
$$
\left\{\begin{aligned}
x^{2}+y & =12 \\
x+y & =12
\end{aligned}\right.
$$
we get the ordered pairs $(0,12)$ and $(1,11)$. That is, the given graphs intersect at $(0,12)$ and $(1,11)$, whose distance is $\sqrt{(0-1)^{2}+(12-11)^{2}}=$ $\sqrt{2}$.