Question 1012475
 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
simplify, divide by 2
4b = 3a
b = 3a/4
b = .75a
:
the difference of their squares is twice their sum.
a^2 - b^2 = 2(a + b)
a^2 - b^2 = 2a + 2b
substitute for b
a^2 - (.75a)^2 = 2a + 2(.75a)
a^2 - .5625a^2 = 2a + 1.5a
Divide equation by a
a - .5625a = 2 + 1.5
.4375a = 3.5
a = 3.5/.4375
a = 8
Find b
b = .75(8)
b = 6
:
 find the numbers. 8 & 6
:
:
:
See if this checks out
8 + 6 = 7(8 - 6)
14  = 7(2)
and
8^2 - 6^2 = 2(8+6)
64 - 36 = 2(14)