Question

For what value of K,the equation k
$kx - 3y + 6 = 0$
,
$4x - 6y + 15 = 0$
represent parallel lines

Answer 1

The answer is given below :

RULE :

The two lines

a1x + b1y + c1 = 0
a2x + b2y + c2 = 0

will represent two parallel lines, if

a1/a2 = b1/b2

SOLUTION :

The given lines are

kx - 3y + 6 = 0
4x - 6y + 15 = 0

These two lines be parallel to each other, if

k/4 = (-3)/(-6)

⇒ k/4 = 1/2

⇒ k = 4/2

⇒ k = 2

Thus, when k = 2, the two given lines be parallel to each other.

Thank you for your question.

Answer 2

Heya!!!

Here's your answer friend,

On comparing above equations we get,

a1 = k, b1 = -3 c1 = 6

a2 = 4, b2 = -6, c = 15

Therefore, condition for Parallel lines,

a1/a2 = b1/b2 ≠ c1/c2

==> k/4 = -3/-6 ≠ 6/15

==> k/4 = 1/2 ≠ 2/5

On Comparing 1st and 2nd we get,

k/4 = 1/2

==> K = 2

Therefore, value of K = 2 for the equations which represents parallel lines.


Hope it helps you : )