Question

Two lines $x+2y+7=0$ and $2x+ky+18=0$ do not intersect each other. Find the value of $k.$

• A. $3$
• B. $2$
• C. $1$
• D. $4$

Answer 1

Answer: (D)

$4$

$x+2y+7=0$ and $2x+ky+18=0$ do not intersect each other, this means that the pair of equations is inconsistent.

On comparing $x+2y+7=0$ with $a_{1}x+b_{1}y+c_1=0$ and $2x+ky+18=0$ with $a_{2}x+b_{2}y+c_2=0$ we get,

$a_1=1,b_1=2,c_1=7,a_2=2,b_2=k,c_2=18$

Thus, we have

$\frac{a_1}{a_2}=\frac{b_1}{b_2}$

$\Rightarrow \frac{1}{2}=\frac{2}{k}$

$\Rightarrow k=4$

Hence, if $k=4$ then the pair of equations will be inconsistent.