5. (35 points) $B$ In the class, an example of adding two integers was written on the board. Top student Petya mentally added these numbers during the break and got 2021. Troublemaker Vasya added a 0 at the end of one of the numbers. When the lesson started, Vasya was called to solve the problem on the board. As a result of the addition, he got 2221. Can you determine if Vasya calculated correctly or not?
Answer: Vasya calculated incorrectly

Solution. Let the integers written on the board be denoted by $x$ and $y$. Then $x+y=2021$. Suppose Vasya added a 0 to the number $x$. If Vasya's subsequent calculations are correct, then $10x + y = 2221$. Subtracting the recorded equations, we get $9x = 200$, which is impossible for any integer $x$.