SOLUTION: If x - y = 14 and x^2 - y^2 = 84, then what is the value of x

Question 1126072: If x - y = 14 and x^2 - y^2 = 84, then what is the value of x
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) x - y = 14
:
2) x^2 - y^2 = 84
:
factor equation 2
:
(x+y) * (x-y) = 84
:
substitute for (x-y) using equation 1
:
(x+y) * 14 = 84
:
x + y = 84/14 = 6
:
3) x + y = 6
:
add equations 1 and 3
:
2x = 20
:
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x = 10 and y = -4
:
check the answers in equations 1 and 2
:
equation 1
:
10 - (-4) = 14
:
14 = 14
:
equation 2
:
10^2 - (-4)^2 = 84
:
100 - 16 = 84
:
84 = 84
:
answers check
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