SOLUTION: Five times a number plus another number is 12. Their difference is 6. What are the two numbers?

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Question 359877: Five times a number plus another number is 12. Their difference is 6. What are the two numbers?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
5x + y = 12.
|x-y| = 6.
y = 12-5x. This implies that |x-(12-5x)| = 6.
|x-12+5x| = 6.
|6x-12| = 6,
|x-2| = 1, after dividing both sides by 6.
Then x-2 = 1 or x-2 = -1. The first equation gives x = 3, and the second, x = 1. If x = 3, y = -3. If x = 1, y = 7. The answers are then (3,-3) or (1,7).