SOLUTION: Hi there, My question is the following: Given that 2^y = 16^(x – 3) and 3^(y+2) = 27^x, find the value of x + y Thank you in advance for your help!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hi there, My question is the following: Given that 2^y = 16^(x – 3) and 3^(y+2) = 27^x, find the value of x + y Thank you in advance for your help!      Log On


   

Question 858971: Hi there,
My question is the following: Given that 2^y = 16^(x – 3) and 3^(y+2) = 27^x, find the value of x + y
Thank you in advance for your help!
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Given that 2^y = 16^(x – 3) and 3^(y+2) = 27^x, find the value of x + y

2^y = 16^(x – 3)
2%5Ey=+2%5E%284%28x-3%29%29
y=4(x-3)
y=4x-12
4x-y=12..................(1)
and 3^(y+2) = 27^x,
3%5E%28y%2B2%29=3%5E%283x%29
y+2=3x
3x-y=2...................(2)
4 x -1 y = 12 .............1
Total value
3 x -1 y = 2 .............2
Eliminate y
multiply (1)by -1
Multiply (2) by 1
-4 x 1 y = -12
3 x -1 y = 2
Add the two equations
-1 x = -10
/ -1
x = 10
plug value of x in (1)
4 x -1 y = 12
40 -1 y = 12
-1 y = 12 -40
-1 y = -28
y = 28
x+y= 28+10=38

find the value of x + y