SOLUTION: how to solve x and y if 2^x × 4^y=1 and 4^xy)=1/16?

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Question 1114412: how to solve x and y if 2^x × 4^y=1 and 4^xy)=1/16?
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


(1) 2%5Ex%2A4%5Ey=1 --> 2%5Ex%2A2%5E%282y%29=1 --> 2%5E%28x%2B2y%29=1 --> x%2B2y=0 --> x+=+-2y

(2) 4%5E%28xy%29=1%2F16 --> xy+=+-2

Substituting (1) into (2),

-2y%5E2+=+-2
y%5E2+=+1
y+=+1 or y+=+-1

(a) y=1 --> x = -2
(b) y = -1 --> x = 2

Answer: 2 solutions: (x,y) = (-2,1) or (x,y) = (2,-1)