SOLUTION: If x^2 - y^2 = 28 and x - y = 8 what is the average of x and y?
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Question 253004: If x^2 - y^2 = 28 and x - y = 8 what is the average of x and y?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x^2 - y^2 = 28 (first equation)
x - y = 8 (second equation)
solve for x in second equation to get:
x = y+8
substitute for x in first equation to get:
x^2 - y^2 = 28 becomes:
(y+8)^2 - y^2 = 28
simplify by performing indicated operations to get:
y^2 + 16y + 64 - y^2 = 28
combine like terms to get:
16y + 64 = 28
subtract 64 from both sides to get:
16y = 28-64 = -36
divide both sides by 16 to get:
y = -36/16
substitute in second equation to get:
x - y = 8 becomes:
x - (-36/16) = 8.
simplify by performing indicated operations to get:
x + 36/16 = 8
subtract 36/16 from both sides to get:
x = 8 - 36/16 = 128/16 - 36/16 = 92/16.
you have:
x = 92/16
y = -36/16
substitute in first equation to get:
x^2 - y^2 = 28 becomes:
(92/16)^2 - (-36/16)^2 = 28
this becomes:
33.0625 - 5.0625 = 28 confirming that the values for x and y are good.
the question was:
what is the average of x and y?
the average of x and y =
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