Question

Find the values of x and y​

Answer 1

Answer:

x = 3, y = 1

Step-by-step explanation:

2 raised to what power gives you 16?

2*2*2*2 = 16 so 2^4

3 raised to what power gives you 9?

3*3 = 9 so 3^2

the exponent cannot be negative so x has to be greater than y and x cannot be the same as y otherwise you will get a 0.

x = 3 , y = 1

2^(3+1) = 2^4 = 16

3^(3-1) = 3^2 = 9

Answer 2

$\:\:\:\:\:\:\:\:\:\:\therefore\bf{x=3\:and\:y=1}$

Solution

$\:\:\:\bf{(2^{x+y},\:3^{x-y})=(16,9)}$

$\sf{Here,}$

$\:\:\:\star\tt{\:\:2^{x+y}=16\:and\:3^{x-y}=9}$

$\sf{Solving,}$

$\:\:\:\implies\tt{\:\:2^{x+y}=16}$

$\:\:\:\implies\tt{\:\:2^{x+y}=2^4}$

$\:\:\:\implies\tt{\:\:x+y=4}$

$\:\:\:\bf{\:\:x=4-y-----(i)}$

$\sf{Solving,}$

$\:\:\:\implies\tt{\:\:3^{x-y}=9}$

$\:\:\:\implies\tt{\:\:3^{x-y}=3^2}$

$\:\:\:\bf{\:\:x-y=2-----(ii)}$

$\sf{Putting\:the\:value\:of\:(i)\:in\:(ii),}$

$\:\:\:\implies\tt{\:\:4-y-y=2}$

$\:\:\:\implies\tt{\:\:4-2y=2}$

$\:\:\:\implies\tt{\:\:-2y=2-4}$

$\:\:\:\implies\tt{\:\:\cancel{-}2y=\cancel{-}2}$

$\:\:\:\implies\tt{\:\:y=\frac{\cancel{2}}{\cancel{2}}}$

$\:\:\:\bf{\:\:y = 1}$

$\sf{Putting\:y = 1\:in\:(i),}$

$\:\:\:\implies\tt{\:\:x=4-1}$

$\:\:\:\bf{\:\:x = 3}$

$\:\:$