Question

Find the value of $k$ or which the following systems of equations be inconsistent.
$2x+ky+k+2=0$; $kx+8y+3k=0$

• A. For $k=2$, given system of equation will have no solution
• B. For$k=-4$, given system of equation will have no solution
• C. For $k=6$, given system of equation will have no solution
• D. For$k=-8,$ given system of equation will have no solution

Answer 1

The correct option is B For$k=-4$, given system of equation will have no solution

Given

$2x+ky+k+2=0$

$kx+8y+3k=0$

For equation to be inconsistent,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Where $a_1,a_2$ are x coefficients

$b_1,b_2$ are y coefficients

$c_1,c_2$ are constants

$\frac{2}{k}=\frac{k}{8}\ne \frac{k+2}{3k}$

$k=\pm 4$ and

$3k^2\ne 8k+16$

$3k^2-8k-16\ne 0$

$3k(k-4)+4(k-4)\ne 0$

$k\ne 4$ and $k\ne \frac{-4}{3}$

$k=-4$ the given system of equations are inconsistent