Answer:
a)x=0 and y=1
b)x=-2 and y=0
Step-by-step explanation:
a)
[tex]3^{x+1}+2^{y+1}=7[/tex]
[tex]3^{x+1}+2^{y+1}=3+4[/tex]
[tex]3^{x+1}+2^{y+1}=3^{1}+2^{2}[/tex]
Hence, x+1=1 and y+1=2
So, x=0 and y=1
To verify, we substitute x and y as 0 and 1, respectively, in second equation
[tex]3^{x}+2^{y-1}=2[/tex]
[tex]3^{0}+2^{1-1}=2[/tex]
[tex]1+2^{0}=2[/tex]
1+1=2
2=2
Hence Verified, that x=0 and y=1
b)
[tex]5^{x+2}+7^{y+1}=8[/tex]
[tex]5^{x+2}+7^{y+1}=5^{0}+7^{1}[/tex] [You might say that it can also be like [tex]5^1+7^0[/tex], but in such case we also have to add 2 ([tex]5^1+7^0+2=8[/tex])]
Hence, x+2=0 and y+1=1
So, x=-2 and y=0
To verify, we substitute x and y as -2 and 0, respectively, in second equation
[tex]5^{x+3}+7^{y}=6[/tex]
[tex]5^{-2+3}+7^{0}=6[/tex]
[tex]5^1+1=6[/tex]
5+1=6
6=6
Hence Verified, that x=-2 and y=0
