Question

Find the value of k for which the system of equations

3x - y = 5, 6x - 2y = k

has no solution

Answer 1

The given system of equations:

3x - y - 5 = 0                      ...(i)

And, 6x - 2y - k = 0          ...(ii)

These equations are of the following form:

a₁x + b₁y + c₁ = 0, a₂x + b₂y + c₂ = 0

where, a₁ = 3, b₁ = -1, c₁ = -5 and a₂ = 6, b₂ = -2, c₂ = -k

In order that the given system has no solution, we must have:

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

`i.e., 3/6 = (−1)/(−2) ≠ (−5)/-k`

⇒ `(−1)/(−2) ≠ (−5)/-k` 

⇒ k ≠ 10

Hence, equations (i) and (ii) will have no solution if k ≠ 10.