The choir director set up chairs for the concert with an equal number of rows and columns.
the number of chairs in each row and column is represented by y,
where y is the total number of chairs. what is the number of chairs in each row and
column if y = 81 chairs?

'y' is NOT the number of chairs in each row and column.  It's the TOTAL number of
chairs, so it's the product of (chairs in each row) times (chairs in each column).
The problem says that those numbers are equal.  So we would expect the TOTAL
to be a perfect square, and the number in each row and each column to be the
square root of the total.  Since the total is 81, the number in each row and column
could be either  +9  or  -9 .  Both answers are mathematically correct, but  -9
doesn't make sense in the real world.  So we know that  +9  is the real answer.