Question

if 2^2x-y=16 and 2^x+y=32. find x * y answer is 6

Answer 1

Given ,

 2^( 2 x - y ) = 16

 2^ ( 2 x - y ) = 2^4

As bases are equal so exponent must be equal,

  2 x - y = 4   -------- eq .1

Now,

  2^ ( x + y ) = 32

  2 ^ ( x + y ) = 2^5

As bases are equal , so exponent must be equal ,

   x + y = 5  ------- eq .2

By adding eq.1 and eq.2,

   2 x - y + x + y = 4 + 5

   3 x = 9

     x = 9 / 3

     x = 3.

By substituting the value of x in eq.2,

    x + y = 5

    3 + y = 5

    y = 5 - 3

    y = 2.

Now , x * y = 3 * 2 = 6.

Therefore , x*y = 6.