Two numbers total 12, and their differences is 20. Find the two numbers.

Two numbers total 12, and their differences is 20. Find the two numbers.

Let the first number be x. Let the second number be y. We're given two equations:

1. x + y = 12
2. x - y = 20

Since we have y coefficients of (-1 and 1) that cancel, we add the two equations together:
(x + x) + (y - y) = 12 + 20

The y terms cancel, so we have:
2x = 32

Type this equation into our search engine and we get:
x = 16

Substitute this value of x = 16 back into equation 1:
16 + y = 12

Typing this equation into our search engine, we get:
y = -4

Now, let's check our work for both equations:

1. 16 - 4 = 12
2. 16 - -4 --> 16 + 4 = 20

So these both check out.
(x, y) = (16, -4)