Question

If kx+2y-1=0 and 6x-4y+2=0 are identical
lines, then determine k.

Answer 1

The value of k = - 3

Step-by-step explanation:

The given linear polynomials are:

kx + 2y - 1 = 0

and  6x - 4y + 2 = 0

Here, $a_{1}=k,[tex]b_{1}=2$and $c_{1}=-1$

$a_{2}=6,b_{2}=-4$and $c_{2}=2$

To find, the value of k = ?

The condition for identical lines,

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

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

⇒  $\dfrac{k}{6}=\dfrac{2}{-4}$ or  $\dfrac{k}{6}=\dfrac{-1}{2}$

⇒ k = - 3 or, k = - 3

Hence, the value of k = - 3