Question

The value of k for which the system of equations 3x – 7y = 1 and kx + 14y = 6 is inconsistent is ______.

Options

• –6

• `2/3`

• 6

• `(-3)/2`

Answer 1

The value of k for which the system of equations 3x – 7y = 1 and kx + 14y = 6 is inconsistent is –6.

Explanation:

3x – 7y = 1

kx + 14y = 6

Here, a₁ = 3, b₁ = –7, c₁ = −1

a₂ = k, b₂ = 14, c₂ = −6

For inconsistent,

`a_1/a_2 = b_1/b_2 ≠ c_1/c_2`

`3/k = (-7)/14 ≠ (−1)/(−6)`

`3/k = (-1)/2 ≠ 1/6`

`3/k = (-1)/2`

−k = 6

k = −6