Question

(2power x+y, 3power x-y) = (16, 9)​

Answer 1

y = 1, x = 3

Explanation:

1.) Based on the given, we have
`2^(x+y)` = 16, and
`3^(x-y)`=9. Since
`2^4` is equal to 16, that means that x + y = 4. Since
`3^2` is equal to 9, that means that x - y = 2

2.) Now, we have a system of equations. By using elimination (adding the two together), you get x + x + y - y = 2 + 4. By simplifying, the y cancels out and you get 2x = 6. Finally, you get x = 3.

3.) To end, you need to find y. Since we have x - y = 2, and x = 3, that means that 3 - y = 2, meaning y = 1.

Answer 2

x = 3 , y = 1

Explanation:

`2^(x+y) = 16\\2^(x+y) = 2^4\\x + y = 4 ---- (1)\\\\3^(x-y) = 9\\3^(x-y) = 3^2\\x-y = 2 ----- (2)\\\\Adding 1 and 2 , we get ,\\ 2x = 6\\x = 3\\y = 1`