Question

Q. If kx+2y-1=0 and 6x-4y+2=0 are identical lines
determine k,
a) -3
b) -1/3
c) 1/3
d) 3​

Answer 1

Given :

• The given identical lines are :

• kx+2y-1=0

• 6x-4y+2=0

To Find :

•The value of k=?

Formula :

If the given two lines are identical lines ,then

$\pink\bigstar\boxed{\bf{\dfrac{a_{1} }{a_{2} }= \dfrac{b_{1} }{b_{2} } = \dfrac{c_{1} }{c_{2} } }}$

Solution :

The given identical lines are :

•kx+2y-1=0

•6x-4y+2=0

Values:

$\bullet\bf{a_{1} =k}$

$\bullet\bf{a_{2}=6}$

$\bullet\bf{b_{1}=2}$

$\bullet\bf{b_{2}=-4}$

$\bullet\bf{c_{1}=-1}$

$\bullet\bf{c_{2}=2}$

By using Formula :

$\implies\sf{\dfrac{a_{1} }{a_{2}}=\dfrac{b_{1}}{b_{2}} =\dfrac{c_{1} }{c_{2} }}$

Substituting the values :

$\implies\sf{\dfrac{k}{6}=\dfrac{2}{-4}=\dfrac{-1}{2}}$

$\implies\sf{\dfrac{k}{6}=-\dfrac{1}{2}}$

$\implies\sf{2k=-6}$

$\implies\sf{k=\dfrac{-6}{2} }$

$\implies\boxed{\sf{k=-3}}$

The value of k is -3