Question

pls send the solution

Answer 1

$4( {2}^{ x- 1} ) + 9( {3}^{y - 1} ) = 17 \\4( \frac{ {2}^{x} }{2} ) +9( \frac{ {3}^{y} }{3} ) = 17 \\ 2( {2}^{x} ) + 3( {3}^{y} ) = 17$
Change :
${2}^{x} = a \\ and \\ {3}^{y} = b$


2a + 3b = 17 [x 3]
3a - 2b = 6 [x 2]
-------------------------
6a + 9b = 51
6a - 4b = 12
----------------------- -
13b = 39
b = 3

2a + 3b = 17
2a + 3(3) = 17
2a + 9 = 17
2a = 17 - 9
2a = 8
a = 4

So....
${2}^{x} = 4 \\ {2}^{x} = {2}^{2} \\ x = 2$


${3}^{y} = 3 \\ {3}^{y} = {3}^{1} \\ y = 1$

Answer : (A) (x, y) = (2, 1)