Problem: Given 2x=8y+12^{x}=8^{y+1}2x=8y+1 and 9y=3x−99^{y}=3^{x-9}9y=3x−9; the value of x+yx+yx+y is:
Answer Choices:
A. 181818
B. 212121
C. 242424
D. 272727
E. 303030 Solution:
2x=8y+1=23(y+1)∴x=3y+3,3x−9=9y=32y∴x−9=2y2^{x}=8^{y+1}=2^{3(y+1)} \quad \therefore x=3 y+3,3^{x-9}=9^{y}=3^{2 y} \quad \therefore x-9=2 y2x=8y+1=23(y+1)∴x=3y+3,3x−9=9y=32y∴x−9=2y
The solution of the two linear equations is x=21,y=6∴x+y=27x=21, y=6 \quad \therefore x+y=27x=21,y=6∴x+y=27