Question

The value of k for which the system of equations 3x − ky = 7 and 6x + 10y = 3 is inconsistent, is ______.

विकल्प

• −10

• −5

• 5

• 7

Answer 1

The value of k for which the system of equations 3x − ky = 7 and 6x + 10y = 3 is inconsistent, is -5.

Explanation:

We know that the system of equations

a₁x + b₁y = c₁

a₂x + b₂y = c₂

For an inconsistent solution, there is only one case where the graphs of the pair of equations are parallel.

Here, a₁ = 3, b₁ = −k, c₁ = 7, a₂ = 6, b₂ = 10, c₂ = 3

`3/6` = `(-k)/10 ≠ 7/3`

`3/6` = `(-k)/10` and `(-k)/10 ≠ 7/3`

−6k = 30 and −3k ≠ 70

k = `(−30)/6` and k ≠ `(-70)/3`

∴ k = −5