Question

He sum of two numbers is 46 and the difference is 2 . What are the numbers?

large number is
the small number is

Answer 1

Let us condense your question in the form of system of equations,

x + y = 46
x - y = 2

Now, x = 46 - y

Thus,

46-y - y = 2

46 - 2y = 2

-2y = -44

Thus, y = 22.

x + y = 46

x + 22 = 46

Thus, x = 24.

Thus, the greater number is 24 and smaller number is 22.

Answer 2

a + b = 46
a-b = 2

solve one of the equations for a...
a + b = 46
a = b + 2

solve for "b" using substitution...
(b + 2) + b = 46
2b + 2 = 46
2b = 44
b = 22

solve for "a" with substitution...
a + (22) = 46
a = 24

Smaller Number: 22
Bigger Number: 24