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!

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) (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)

y=4(x-3)
y=4x-12
4x-y=12..................(1)
and 3^(y+2) = 27^x,

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

RELATED QUESTIONS
Hello, Please help me with the following as I am completely stuck on it and google... (answered by josmiceli,mananth)

Hi there. I have been stuck on this for hours! Here is the following question. The... (answered by Earlsdon,stanbon,jim_thompson5910)

Thank you in advance tutor,I would like to ask you this proportion question Given that y (answered by stanbon,josmiceli)

If x+y+z=16 then find the maximum value of (x-3)(y-5)(z-2). Given that (x-3)>0,... (answered by Edwin McCravy,ikleyn)

If x+y=16 and xy=3, find the value of a) x^2 +y^2 b)... (answered by ikleyn,josgarithmetic)

(x^y)=(y^x) ; (x^2)=(y^3) Find out the value of x and... (answered by math_helper)

i would really be thank u if u could help me out with this. thank so much Identify (answered by stanbon)

Hi there, Im having trouble with this question: f(x)= X^2 - 4x +3 I need help... (answered by Fombitz)

Hi I'm Kelly and my question is, Use the properties of logarithms to condense the... (answered by Alan3354)