SOLUTION: The sum of two numbers is 5 times their difference. If one exceeds the other by 7, what are the numbers?

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Question 186548: The sum of two numbers is 5 times their difference. If one exceeds the other by 7, what are the numbers?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

1st condition:
x%2By=5%28x-y%29
2nd condition:
x=y%2B7, ---->subst. in Condtn 1:
.
x%2By=5x-5y
y%2B7%2By=5%28y%2B7%29-5y
2y%2B7=5y%2B35-5y--->2y=cross%285y%29%2B35-cross%285y%29-7
2y=28--->cross%282%29y%2Fcross%282%29=cross%2828%2914%2Fcross%282%29
highlight%28y=14%29
Then in Condtn 2:
x=14%2B7---->highlight%28x=21%29
Let's check via Condtn 1:
The sum of 2 numbers---->14%2B21=35
Equals 5 times their difference:
35=5%2821-14%29%29
35=5%287%29
35=35
Thank you,
Jojo