Question

The value of k for which the system of equations 3x − y + 8 = 0 and 6x − ky + 16 = 0 has infinitely many solutions, is ______.

पर्याय

• −2

• 2

• `1/2`

• `−1/2`

Answer 1

The value of k for which the system of equations 3x − y + 8 = 0 and 6x − ky + 16 = 0 has infinitely many solutions, is 2.

Explanation: 

Given equation are 

3x − y + 8

6x − ky + 16 = 0

a₁ = 3, b₁ = −1, c₁ = 8

a₂ = 6, b₂ = −k, c₂ = 16

For infinitely many solutions

`a_1/a_2 = b_1/b_2 = c_1/c_2`

⇒ `3/6 = (-1)/-k`

⇒ `1/2 = 1/k`

⇒ k = 2