SOLUTION: Given {{{2^x=8^(y+1)}}} and {{{9^y=3^(x-9)}}}, find the values of x+y.

Algebra ->  Expressions-with-variables -> SOLUTION: Given {{{2^x=8^(y+1)}}} and {{{9^y=3^(x-9)}}}, find the values of x+y.      Log On


   

Question 468345: Given 2%5Ex=8%5E%28y%2B1%29 and 9%5Ey=3%5E%28x-9%29, find the values of x+y.
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
From the first equation 2%5Ex=8%5E%28y%2B1%29
2%5Ex=2%5E%283%28y%2B1%29%29
So, x=3%28y%2B1%29
From the second equation 9%5Ey=3%5E%28x-9%29
3%5E%282y%29=3%5E%28x-9%29
2y=x-9
System
system%28x=3%28y%2B1%29%2C2y=x-9%29
system%28x-3y=3%2Cx-2y=9%29,
Subtract the second equation from the first one
-y=-6
y=6
Put y=6 in the first equation
x-3%2A6=3
x=21
system%28x=21%2Cy=6%29
x%2By=21%2B6=27
Answer: 27