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 =