Question

for what value of K, the following system of equations represent parallel lines ? kx-3y+6=0,4x-6y+15=0​

Answer 1

Answer:

k = 2

Step-by-step explanation:

kx - 3y + 6 = 0 --------- (i)

4x - 6y + 15 = 0 ------- (ii)

Here, a1 = k , b1 = -3 , c1 = 6

a2 = 4 , b2 = -6 , c2 = 15

a1/a2 = k/4

b1/b2 = -3/-6 = 1/2

c1/c2 = 6/15 = 2/5

For parallel lines,

a1/a2 = b1/b2 is not equal to c1/c2

:. k/4 = 1/2

2k = 4

k = 4/2 = 2

Hence the value of k is 2

Answer 2

k = 2

Step-by-step explanation:

kx - 3y + 6 = 0 --------- (i)

4x - 6y + 15 = 0 ------- (ii)

Here, a1 = k , b1 = -3 , c1 = 6

a2 = 4 , b2 = -6 , c2 = 15

a1/a2 = k/4

b1/b2 = -3/-6 = 1/2

c1/c2 = 6/15 = 2/5

For parallel lines,

a1/a2 = b1/b2 is not equal to c1/c2

:. k/4 = 1/2

2k = 4

k = 4/2 = 2

Hence the value of k is 2