Eight, (Full marks 10 points) A student buys a certain type of pencil. When he buys $x$ pencils, he pays $y$ yuan ($x, y$ are both integers). The clerk says: "If you buy 10 more, I will charge you a total of 2 yuan. This way, for every 30 pencils you buy, you can save 2 yuan." Find $x$ and $y$.

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Eight, according to the salesperson, $y$ can only be 1 or 2.
(1) When $y=1$, according to the problem, the original price per item is $\frac{1}{x}$ yuan. Buying 10 more items saves $\frac{1}{15}$ yuan per item, so the current price per item is $\frac{1}{x}-\frac{1}{15}$ (yuan).
Let the total number of items after buying 10 more be $m$. Then we have $\left(\frac{1}{x}-\frac{1}{15}\right) \times m=2$.
At this point, $m$ can only be $15, 30, 45, 60, \cdots$
After discussion, only when $m=15, x=5$, does it meet the requirements of the problem.
(2) When $y=2$, we know that $\left(\frac{2}{x}-\frac{2}{15}\right) \times m=2$.
No matter what integer $m$ is, it does not meet the requirements of the problem.
Therefore, the solution to this problem is $x=5, y=1$.