Question

The pair of lines represented by the equations $2x+y+2=0$ and $4x+ky+6=0$ will be parallel if value of $k$ is:

Answer 1

Finding the value of k:

• It is known that two lines $l_{1}and{l}_2$ are parallel if they are in a form of $ax+by=c$ and $ax+by=d$, that is, the coefficients of $x\mathrm{and}y$ must be the same.
• Here, $a,b,c\mathrm{and}d$ are constants.

It is given that the equations written below are parallel:

$\begin{array}{rcl}2x+y+2& =& 0...\left(1\right)\\ 4x+ky+6& =& 0...\left(2\right)\end{array}$

Take 2 as common from equation (2):

$$\begin{gathered} 2\left(2x+\frac{ky}{2}+3\right)=0 \\ \Rightarrow 2x+\frac{ky}{2}+3=0 \\ \Rightarrow 2x+\frac{ky}{2}=-3...\left(3\right) \end{gathered}$$

Similarly, rewrite the equation (1) as follows:

$2x+y=-2$ …(4)

As the coefficient should be same therefore, on comparing equations (3) and (4):

$$\begin{gathered} \frac{k}{2}=1 \\ \Rightarrow k=2 \end{gathered}$$

Final Answer:

Hence, the value of k is 2.