The sum of two numbers is 8. their difference is 12. find the numbers.

let the two numbers be: x y

x + y = 8

x - y = 12

Isolate the x in x + y = 8. Subtract y from both sides

x + y (-y) = 8 (-y)

x = 8 - y

Plug in 8 - y for x in the other equation

x - y = 12

(8 - y) - y = 12

Simplify

8 -2y = 12

Isolate the y. Subtract 8 from both sides, and then divide by -2

8 (-8) - 2y = 12 (-8)

-2y = 4

-2y/-2 = 4/-2

y = -2

Plug in -2 for y in one of the equations

x + y = 8

x + (-2) = 8

Simplify. Isolate the x. Add 2 to both sides

x - 2 (+2) = 8 (+2)

x = 10

x = 10, y = -2 is your answer

hope this helps

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