Question

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

Answer 1

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.)