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

Algebra ->  Equations -> SOLUTION: If x - y = 14 and x^2 - y^2 = 84, then what is the value of x      Log On


   

Question 1126072: If x - y = 14 and x^2 - y^2 = 84, then what is the value of x
Answer by rothauserc(4718) About Me  (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
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substitute for (x-y) using equation 1
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(x+y) * 14 = 84
:
x + y = 84/14 = 6
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3) x + y = 6
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add equations 1 and 3
:
2x = 20
:
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x = 10 and y = -4
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check the answers in equations 1 and 2
:
equation 1
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10 - (-4) = 14
:
14 = 14
:
equation 2
:
10^2 - (-4)^2 = 84
:
100 - 16 = 84
:
84 = 84
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answers check
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