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

Assessment: JAMB UTME - Mathematics - 2019 Subject: General Mathematics

Question 1 Report

x =

\frac{3}{4}

, y =

\frac{11}{4}

x =

\frac{3}{4}

, y =

\frac{13}{4}

x =

\frac{2}{3}

, y =

\frac{4}{5}

x =

\frac{2}{3}

, y =

\frac{13}{4}

Answer Details

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