SOLUTION: the sum of two numbers is 16, and the difference is 6, what is their product? cannot be 60

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Question 421066: the sum of two numbers is 16, and the difference is 6, what is their product? cannot be 60
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
We have a%2Bb+=+16 and a-b+=+6. There are two solutions:

Solution 1:
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We can solve the system by adding both equations to produce 2a+=+22 --> a+=+11. Replace a with 11 in either equation to get b+=+5, ab+=+55.

Solution 2:
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We can square both equations to obtain
a%5E2+%2B+2ab+%2B+b%5E2+=+256
a%5E2+-+2ab+%2B+b%5E2+=+36

Subtracting the second equation from the first, we obtain 4ab+=+220 which implies ab+=+55.