If (0, 1,2, x ,4,3,6,y,7) is the possible set of residues, mod 9(x<y). Find the value of x and y

The complete set of residues modulo 9 consists of all non-negative integers less than 9.
This set is $\{0, 1, 2, 3, 4, 5, 6, 7, 8\}$.

The given set is $(0, 1, 2, x, 4, 3, 6, y, 7)$.
Let's list the known elements from the given set in ascending order: $\{0, 1, 2, 3, 4, 6, 7\}$.

By comparing the known elements from the given set with the complete set of residues modulo 9, we can see which numbers are missing.
Missing elements = $\{0, 1, 2, 3, 4, 5, 6, 7, 8\} - \{0, 1, 2, 3, 4, 6, 7\} = \{5, 8\}$.
Therefore, $x$ and $y$ must be 5 and 8.

Given that $x < y$, we assign the smaller missing value to $x$ and the larger missing value to $y$.
So, $x = 5$ and $y = 8$.

The values are: