Final answer:
The correct equations based on the given information are 12.99x + 9.98y = 1,012.58 and x + y = 90, which express the relationship between the quantity and cost of the T-shirts sold and the total number of T-shirts sold, respectively.
Step-by-step explanation:
The equations that represent the given information accurately are 12.99x + 9.98y = 1,012.58 and x + y = 90. The first equation represents the total dollar amount of shirts sold, with x being the number of long-sleeve T-shirts sold at $12.99 each and y being the number of short-sleeve T-shirts sold at $9.98 each. The second equation represents the total number of T-shirts sold, where again, x is the number of long-sleeve T-shirts and y is the number of short-sleeve T-shirts. Together, these two equations can be used to solve for the variables x and y.