The sum of two numbers is 56 and the difference is 20. What are the numbers

38+18 = 56 and 38-18=20

x + y is 56 or

x+y=56

the difference means you subtract them ...

so

x-y = 22

you have two equations and two unknowns, you can use elimination or substitution

x+y=56

x-y = 22

add the 2 equations together ...

x+y=56

x-y = 22

and I get:

2x = 78 divide both side by 2

x = 78/2 = 39

substitute this back into the original equations (anyone of them) to find what y is equal to.

x+y=56

39 + y = 56

y = 56-39 = 17

so you get : x = 39, y = 17

check your answers by substituting

x+y=56 39+17 = 56 check

x-y = 22 39 - 17 = 22 check