The sum of two numbers is 15 and the difference is 19. What are the numbers?

X+y=47

x-y=15

add the equations

2x=62

x=31

31+y=47

y=16

31 and 16 are the numbers

also, ...

x and 47-x are the numbers

x - (47-x) = 15

x-47+x=15

2x-47=15

2x=47+15

2x=62

x=31

47-x=47-31=16

if you are in a lower level course ...

47/2=23.5

use 23 and 24 to begin

their sum is 47 but their difference is not 15

23 and 24

22 and 25

21 and 26

20 and 27

19 and 28

18 and 29

17 and 30

16 and 31 are the numbers