Question

The pair of lines represented by the equations 2x+y+3 =0 and 4x+ky+6 =0 will be parallel if value of k is ​

Answer 1

Answer:

If the value of k is 2 then the pair of lines will be parallel.

Step-by-step explanation:

If a pair of lines is parallel then their slopes are equal.

Let m and m1 be their slope.

For parallel lines, m = m1 .... Formula

Finding slope of 2x+y+3 =0,

2x + y + 3 =0 in the form of y = mx + c is 2x + y = -3

Therefore,

1 = m(2) + (-3)

1 = 2m - 3

2m = 3 + 1

m = 4/2

m = 2 ..... (1)

Similarly, finding slope of 4x+ky+6 =0,

4x+ky+6 =0 in the form of y = mx + c is 4x + ky = -6

Therefore,

k = m(4) + (-6)

k = 4m - 6

m1 = (k + 6) / 4 .... (2)

m = m1

2 = (k + 6) / 4

2 x 4 = (k + 6)

8 = k + 6

k = 8 - 6

k = 2