If 2^(x+y )=16 and 4^(x-y )=1/32, find the values of x and y.

If 2^(x+y )=16 and 4^(x-y )=1/32, find the values of x and y.
A. x = 3/4, y = 11/4
B. x = 3/4, y = 13/4
C. x = 2/3, y = 4/5
D. x = 2/3, y = 13/4

Correct Option: Answer is B

Solution:
2^(x+y )=16 ; 4^(x-y )=1/32
= 2^(x+y )=2^4
x +y = 4….(1)
= 2^(2(x-y) )=2^(-5)
2x – 2y = -5 ….(2)
Solve simultaneously,
x +y = 4
2x – 2y = -5
X = ¾ ; y = 13/4

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