Question

find the value of x and y from the equal ordered pairs :
( 2^x+y , 2^x-y) = (16 , 1)​

Answer 1

Answer:

x = 2   ;    y = 2

Step-by-step explanation:

Given, ( 2^x + y , 2^ x - y ) = ( 16 , 1 )

 This can be true only when 2^( x + y ) = 16 and 2^( x - y ) = 1

Therefore,

2^( x + y ) = 16    &   2^( x - y ) = 1

2^( x + y ) = 2^4   & 2^( x - y ) = 2^0

         Comparing bases and powers:

⇒ x + y = 4    & x - y = 0

⇒ x + y = 4    & x = y

      ⇒ x + x = 4

      ⇒ 2x = 4   ⇒ x = 2

Hence,

 x = y = 2