Question

If 2 X + 3 y + 5 = 0,Kx+ 6y + 7 = 20 are parallel then the value of k is

Answer 1

Given two equations -

2x + 3y + 5 = 0

kx + 6y + 7 = 20 ______( 1 )

On further solving ( 1 )

kx + 6y + 7 - 20 = 0

kx + 6y - 13 = 0

a1 = 2, a2 = k, b1 = 3, b2 = 6, c1 = 5, c2 = - 13

Condition for parallel lines -

a1 / a2 = b1 / b2

Putting values

2 / k = 3 / 6

2 / k = 1 / 2

k = 2 × 2

k = 4

^^'

Answer 2

2x + 3y + 5 = 0 .........(1)

kx + 6y + 7 = 20

kx + 6y + 7 - 20 = 0

kx + 6y - 13 .......(2)


In the above equations (1) and (2)


a1 = 2x , a2 = kx

b1 = 3y , b2 = 6y

c1 = 5 , c2 = - 13


We have to find k....


Now, it is given that they are in parallel line then,


$\frac{a1}{a2}$ = $\frac{b1}{b2}$

$\frac{2x}{kx}$ = $\frac{3y}{6y}$

$\frac{2}{k}$ = $\frac{3}{6}$

$3k = 12$


$\textbf{k = 4}$