Question

for what value of k does the pair of equations 8x + 2y = 5k and 4x + y = 3 represent coincident lines?

Answer 1

Answer:

k = 6/5

Step-by-step explanation:

Condition for Coincident lines:

• $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$

Given Equations:

• 8x + 2y - 5k = 0
• 4x + y - 3 = 0

Here, a₁ = 8, a₂ = 4, b₁ = 2, b₂ = 1, c₁ = -5k, c₂ = -3

Now according to the condition,

$\implies \dfrac{8}{4} = \dfrac{2}{1} = \dfrac{ -5k}{-3}\\\\\implies \dfrac{2}{1} = \dfrac{5k}{3}$

Cross multiplying we get,

$\implies 5k \times 1 = 2 \times 3\\\\\implies 5k = 6\\\\\implies k = \dfrac{6}{5}$

Hence value of k must be 6/5.

Hope it helped !!

Answer 2

Answer:

Step-by-step explanation

Condition for Coincident lines:

Given Equations:

8x + 2y - 5k = 0

4x + y - 3 = 0

Here, a₁ = 8, a₂ = 4, b₁ = 2, b₂ = 1, c₁ = -5k, c₂ = -3

Now according to the condition,

Cross multiplying we get,

Hence value of k must be 6/5.

Hope it helped !!