SOLUTION: i need help in solving this problem: the sum of two numbers is 7 times their difference. the difference of their squares is twice their sum. find the numbers

Question 701293: i need help in solving this problem: the sum of two numbers is 7 times their difference. the difference of their squares is twice their sum. find the numbers
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the sum of two numbers is 7 times their difference.
a + b = 7(a-b)
a + b = 7a - 7b
b + 7b = 7a - a
8b = 6a
b = a
b = .75a
:
the difference of their squares is twice their sum.
a^2 - b^2 = 2(a+b)
a^2 - b^2 = 2a + 2b
replace b with .75a
a^2 - (.75a)^2 = 2a + 2(.75a)
a^2 - .5625a^2 = 2a + 1.5a
a^2 - .5625a^2 = 3.5a
Divide thru by a
a - .5625a = 3.5
.4375a = 3.5
a = 3.5/.4375
a = 8
:
Find b
b = .75(8)
b = 6
:
:
You can confirm this in the original statements

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