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

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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)