Question

9. 2x + 3y = 5 and 4x + ky = 8 pair of linear equations has uniqu
solution. Then
A) k#2 B) k24 C) k#6 D) k = 8​

Answer 1

Answer:

C ) k ≠ 6

Step-by-step explanation:

Given pair of linear equations

• 2x + 3y = 5
• 4x + ky = 8

For the equations to have unique solution

• a(1) / a(2) ≠ b(1) / b(2)

Comparing the given pair of equations with a(1) x + b(1) y = c(1) and a(2) x + b(2) y = c(2) we get,

• a(1) = 2
• a(2) = 4
• b(1) = 3
• b(2) = k

⇒ a(1) / a(2) ≠ b(1) / b(2)

⇒ 2 / 4 ≠ 3 / k

⇒ 1 / 2 ≠ 3 / k

⇒ k ≠ 3 × 2

⇒ k ≠ 6

Therefore the given equation has unique solution for all real values of k except 6 i.e k ≠ 6 ( Option C )

Answer 2

Answer:

C ) k ≠ 6

Step-by-step explanation:

Given pair of linear equations

• 2x + 3y = 5
• 4x + ky = 8

For the equations to have unique solution

• a(1) / a(2) ≠ b(1) / b(2)

Comparing the given pair of equations with a(1) x + b(1) y = c(1) and a(2) x + b(2) y = c(2) we get,

• a(1) = 2
• a(2) = 4
• b(1) = 3
• b(2) = k

⇒ a(1) / a(2) ≠ b(1) / b(2)

⇒ 2 / 4 ≠ 3 / k

⇒ 1 / 2 ≠ 3 / k

⇒ k ≠ 3 × 2

⇒ k ≠ 6

Therefore the given equation has unique solution for all real values of k except 6 i.e k ≠ 6 ( Option C )

Answer 3

Answer:

C ) k ≠ 6

Step-by-step explanation:

Given pair of linear equations

• 2x + 3y = 5
• 4x + ky = 8

For the equations to have unique solution

• a(1) / a(2) ≠ b(1) / b(2)

Comparing the given pair of equations with a(1) x + b(1) y = c(1) and a(2) x + b(2) y = c(2) we get,

• a(1) = 2
• a(2) = 4
• b(1) = 3
• b(2) = k

⇒ a(1) / a(2) ≠ b(1) / b(2)

⇒ 2 / 4 ≠ 3 / k

⇒ 1 / 2 ≠ 3 / k

⇒ k ≠ 3 × 2

⇒ k ≠ 6

Therefore the given equation has unique solution for all real values of k except 6 i.e k ≠ 6 ( Option C )