Question

For what value of K, the following pair of linear equation has infinitely many solution
$Kx+4y=(\mu +8)=0$
4x + ky + 4 = 0

Answer 1

Given lines

kx + 4y + (4+8) = 0

4x + ky + 4= 0

for lines to have infinite solutions

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ $[a_{1}x+b_{1}y+c_1=0,a_{2}x+b_{2}y+c_2=0]$

$\therefore \frac{k}{4}=\frac{4}{k}=\frac{\mu +8}{4}$

$\therefore \frac{k}{4}=\frac{4}{k}\Rightarrow k^2=16$ k=4 $\frac{4}{k}=\frac{\mu +8}{4}$

$k=\pm 4$ $\frac{4}{4}=\frac{\mu +8}{4}$

$k=-4\Rightarrow \frac{4}{-4}=\frac{\mu +8}{4}$ $\mu =-4$

$=\mu =-12$

$\therefore$ for $k=\pm 4$ The line has infinite solutions