SOLUTION: The difference of two positive numbers is 3 and their difference of their squares is 69. Find the numbers.

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Question 1059723: The difference of two positive numbers is 3 and their difference of their squares is 69. Find the numbers.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The difference of two positive numbers is 3 and their
difference of their squares is 69. Find the numbers.

system%28x-y=3%2Cx%5E2-y%5E2=69%29

Factor the left side of the second equation:

%28x-y%29%28x%2By%29=69%29

Use the first equation to substitute 3 for (x-y)

3%28x%2By%29=69%29

Divide both sides by 3

x%2By=23%29

Our system of equations is now:

system%28x-y=3%2Cx%2By=23%29

Add the equations term by term:

2x=26%29

x=13%29

Substitute in 

x-y=3

13-y=3

-y=-10

y=10

Answer: 13 and 10

Edwin