Question

Solve the following systems of equations.
$2^x+2^y=12,x+y=5$

Answer 1

Solve $2^x+2^y=12...\left(1\right)$

$x+y=5...\left(2\right)$

short

simply we take $x=2,y=3$ these eq. satiesfied

as Eq (1) $2^2+2^3=4+8=12$

Eq (2) & $2+3=5$

Now

by eq (2) $y=5-x$ put in eq (1)

$2^x+2^{(5-x)}=12$

$2^x+2^5{.2}^{-x}=12$

$2^{2x}+2^5={12.2}^x$

$(2^x{)}^2-12.(2^x)+32=0$

Let $2^x=t$

$t^2-12t+32=0$

$\Rightarrow (t-8)(t-4)=0$

$\Rightarrow t=8,t=4$

$\Rightarrow 2^x=2^3$ & $2^x=2^2$

$\Rightarrow x=3$ and $x=2$

similarly by eq. (2) $x=5-y$ and put in eq (1)

by above simplification as for x

we get $y=2$ and $x=3$

Hence solution $x=3,y=2$

and $x=2,y=3$ Sol.