Question

Solve by elimination method :-

Answer 1

Hey Tanu !

Here is your solution :

2^x + 3^y = 17 ------- ( 1 )

2^( x + 2 ) - 3^( y + 1 ) = 5 ------- ( 2 )


By multiplying in ( 1 ) by 3,

( 2^x ) 3 + ( 3^y ) 3 = 51

( 2^x )3 + 3^( y + 1 ) = 51 -------- ( 3 )

Adding ( 2 ) and ( 3 ),

2^( x + 2 ) - 3^( y + 1 ) = 5

( 2^x ) 3 + 3^( y + 1 ) = 51

_____________________

2^( x + 2 ) + 2^( x ) 3 = 51 + 5

By taking, 2^x as common in L.H.S,

( 2^x ) ( 2^2 + 3 ) = 56

( 2^x ) ( 4 + 3 ) = 56

( 2^x ) 7 = 56

2^x = 56 ÷ 7

2^x = 8

2^x = ( 2)^3


As bases are equal, so exponent will be also equal.

x = 3.


By substituting the value of x in ( 1 ),

2^x + 3^y = 17

2^3 + 3^y = 17

8 + 3^y = 17

3^y = 17 - 8

3^y = 9

3^y = 3^2

As bases are equal, so exponent will be also equal.

y = 2.



So, x = 3 and y = 2.


===================================


Hope it helps !!

Answer 2

heya here is your answer please mark me as brainlest