SOLUTION: two numbers differ by 9. the sum of their squares is 653. what are the numbers

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Question 1163920: two numbers differ by 9. the sum of their squares is 653. what are the numbers
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28x-y=9%2Cx%5E2%2By%5E2=653%29
-
x%5E2-2xy%2By%5E2=653-2xy
x%5E2%2By%5E2=653-2xy
.
.
286=xy

Look at first equation and see x=y%2B9.
Substitute.
286=y%28y%2B9%29------------factorize and look for if possible two factors differing by 9.

286=highlight%2822%2A13%29

13 and 22

OR

-13 and -22