SOLUTION: one positive integer is 6 less than twice a number. the sum of their squares is 164. find the integers

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Question 769223: one positive integer is 6 less than twice a number. the sum of their squares is 164. find the integers
Answer by Jc0110(165) About Me  (Show Source):
You can put this solution on YOUR website!
Let the positive integer to be x whereas the number to be y.
x=2y-6 ---> Equation 1 ... Substitute into Equation 2
x%5E2%2By%5E2=164 ---> Equation 2
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%282y-6%29%5E2%2By%5E2=164
%284y%5E2-24y%2B36%29%2By%5E2=164
4y%5E2-24y%2B36%2By%5E2=164
4y%5E2%2By%5E2-24y%2B36-164=0
5y%5E2-24y-128=0
%285y%2B16%29%28y-8%29=0
y=-16%2F5 or y=8
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If y=-16%2F5, x=2%28-16%2F5%29-6=-12%262%2F5
* x=-12%262%2F5 is not the answer as x must be a positive integer.
If y=8, x=2%288%29-6=10
* x=10 is the answer as x is a positive integer.
Thus, the integer is 10.