If 2x+y x + y = 16 and 4x−y=132 x − y = 1 32 , find the values of x and y.

If 2${}^{x+y}$ = 16 and 4${}^{x-y}=\frac{1}{32}$, find the values of x and y.

Answer Details

2${}^{x+y}$ = 16 ; 4${}^{x-y}$ = $\frac{1}{32}$.
$⟹2^{x+y}=2^4$
$x+y=4...\left(1\right)$
$2^{2(x-y)}=2^{-5}$
$2^{2x-2y}=2^{-5}$
$⟹2x-2y=-5...\left(2\right)$
Solving the equations (1) and (2) simultaneously, we have
x = $\frac{3}{4}$ and y = $\frac{13}{4}$