8.1. The graphs of the functions $y=a x+b$ and $y=c x+d$ intersect at the point with coordinates $(1 ; 0)$. Compare the values of the expressions $a^{3}+c^{2}$ and $d^{2}-b^{3}$?
Answer: they are equal.

Solution: Since the graphs pass through the point with coordinates $(1 ; 0)$, then $0=a+b$ and $0=c+d$. Therefore, $a=-b$, and $c=-d ; a^{3}+c^{2}=(-b)^{3}+(-d)^{2}=-b^{3}+d^{2}=d^{2}-b^{3}$. Thus, the values of the expressions $a^{3}+c^{2}$ and $d^{2}-b^{3}$ are equal.

Criteria: Only the answer - 0 points. If it is correctly found that $a=-b$ and $c=-d$, but there is no further progress in the solution (or the solution is incorrect thereafter) - 2 points. 7 points for a fully correct solution.