Question

The value of k for which the system of linear equations `x/2 + y/3 = 5` and 2x + ky = 7 is inconsistent, is ______.

Options

• `3/4`

• `4/3`

• `1/3`

• 3

Answer 1

The value of k for which the system of linear equations `x/2 + y/3 = 5` and 2x + ky = 7 is inconsistent, is `underlinebb(4/3)`.

Explanation:

A system of linear equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is inconsistent (no solution) if the lines are parallel.

`x/2 + y/3 - 5 = 0`

3x + 2y – 30 = 0   ...(i)

2x + ky – 7 = 0   ...(ii)

Comparing coefficients:

a₁ = 3, b₁ = 2, c₁ = –30

a₂ = 2, b₂ = k, c₂ = –7

Condition for inconsistency:

`(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)`

Apply the first part of the condition:

`3/2 = 2/k`

3k = 4

`k = 4/3`

Check the second part:

`3/2 ≠ (-30)/(-7)`, which is 1.5 ≠ 4.28

The value of k is `4/3`.