Question

For what value of ‘k’ the given pair of linear equations are parallel : 2x+3y=5 , 4x+ky=8​

Answer 1

Step-by-step explanation:

if k=6 this pair of equations does not have a solution.

therefore, the lines will be parallel.

Answer 2

Answer :-

The value of k = 6

Explanation :-

Consider 2 linear equations as:

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

For lines to be parallel,

$\sf{ \dfrac{a _{1}}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}}$

In the given question,

• a₁ = 2
• a₂ = 4
• b₁ = 3
• b₂ = k

a₁ ÷ a₂ = b₁ ÷ b₂

⇒ 2 ÷ 4 = 3 ÷ k

⇒ 3/k = 1/2

⇒ k = 3 × 2

⇒ k = 6

∴ k = 6

KNOW MORE:

• For lines to be coincident,

a₁/a₂ = b₁/b₂ = c₁/c₂