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