The difference between two numbers is 9999. seven times the smaller is equal to 33 more than the larger. what are the numbers?

x-y=9999

7y=33+x

This is the same as a system of linear equations.

Solve by substitution method;

x - (x+33) / 7=9999 multiply each side by 7 to make common denominators equal:

7x-x+33 = 69993

6x=69993-33

6x=69960

x = 11660

Put x in the top equation (x-y=9999)

11660-y = 9999

11660-9999 = y

y=1661

x=11,660 and y=1661 (they're your numbers.)