Question

if The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 4
will have infinitely many solutions, then value of c = ________ (3, -3,–12)​

Answer 1

Answer:

The value of c is 3.

Step-by-step-explanation:

The given linear equations are

cx - y = 2

⇒ cx - y - 2 = 0 - - - ( 1 )

6x - 2y = 4

⇒ 6x - 2y - 4 = 0 - - - ( 2 )

Comparing equation ( 1 ) with a₁x + b₁y + c₁ = 0, we get,

• a₁ = c
• b₁ = - 1
• c₁ = - 2

Comparing equation ( 2 ) with a₂x + b₂y + c₂ = 0, we get,

• a₂ = 6
• b₂ = - 2
• c₂ = - 4

For system of linear equations to have infinitely many solutions,

a₁ / a₂ = b₁ / b₂ = c₁ / c₂

⇒ a₁ / a₂ = b₁ / b₂

⇒ c / 6 = - 1 / - 2

⇒ c * ( - 2 ) = ( - 1 ) * 6

⇒ - 2c = - 6

⇒ 2c = 6

⇒ c = 6 / 2

⇒ c = 3

∴ The value of c is 3.