Question

for what value of k the following system of equations represents a pair of parallel lines? 2x + ky = 10 , x + (k + 3)y = 12​

Answer 1

Answer:

6

the condition for parallel lines is

a1/ a2 = b1/b2

2/3= k/k+3

cross multiplication

3k = 2 (k+3)

3k = 2k +6

3k - 2k = 6

k = 6

hope this helps you..

Answer 2

The system of equations given are :

➱ 2x + ky = 10

➱ x + (k + 3)y = 12

On comparing these equations to ax + by + c, we get :

↦ a₁ = 2

↦ b₁ = k

↦ c₁ = – 10

↦ a₂ = 1

↦ b₂ = k + 3

↦ c₂ = – 12

We know that, if a₁/a₂ = b₁/b₂ then the equations represent a pair of parallel lines.

So, let's substitute :

➱ 2/1 = k/k + 3

Cross multiplying them and solving :

↦ 2 (k + 3) = k

↦ 2k + 6 – k = 0

↦ k + 6 = 0

↦ k = – 6

Therefore, the value of k is – 6 for the given system of equations representing a pair of parallel lines.