Hi, You are absolutely correct 

4^x (2^y)=16

(2^2x)(2^y) = 2^4

In general, 

 2^(2x+y) = 2^4      both sides of equation with the same base

      Exponents are also equal



8^x= 2^(y/2)

 2^3x = 2^(y/2)

   3x = y/2

   6x = y



   2x + y = 4

   2x + 6x = 4  Substituting  6x for y

       8x = 4  

        x = 1/2   y = 3   (6*(1/2) 

RELATED QUESTIONS

Solve for x and y      simultaneously    x+y=2    and... (answered by Fombitz)

Solve for x and y simultaneously:
y-x=-1... (answered by Boreal)

Solve for the unknowns simultaneously:
2logy = log2 + logx and 2^y = 4^x
 (answered by jim_thompson5910,scott8148)

simultaneously equations y=-x+3 and... (answered by Alan3354)

Please help me solve for x and y simultaneously {{  y-2x+1 and... (answered by Alan3354)

Simultaneously solve y=x^2-2x-3 and... (answered by Fombitz)

Solve the following simultaneously 

[ 2 / (x+y) ] +  [1 / (y-x) ] = 8
[ 1 / (x+y) ] +  (answered by josgarithmetic)

2*x/y=1/8,solve for x and... (answered by Alan3354,josgarithmetic)

Solve this system for (x, y) :  2^x.4^y = 16  and 4^3x-2.(1/2)^y =... (answered by vksarvepalli)