SOLUTION: One number is six larger than another number. The square of the larger number is 132 greater than the square of the smaller number. What are the numbers?

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Question 821762: One number is six larger than another number. The square of the larger number is 132 greater than the square of the smaller number. What are the numbers?
Answer by jhunjiro(67) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
x = larger number
y = smaller number
-
x=y%2B6eq 1
x%5E2=y%5E2%2B132eq 2
-
Solution:
substitute eq 1 to eq 2
%28y%2B6%29%5E2=y%5E2%2B132
-
y%5E2%2B12y%2B36=y%5E2%2B132
-
y%5E2-y%5E2%2B12y=132-36
-
12y=96
-divide both sides by 12
highlight+%28y=8%29 smaller number
-
x=8%2B6
highlight+%28x=14%29 larger number