Question

Find the value of k for which the following system of equations has a unique solution:

5x – 7y – 5 = 0, 2x + ky – 1 = 0

Answer 1

The given system of equations is

5x – 7y – 5 = 0   ...(i)

2x + ky – 1 = 0   ...(ii)

This system is of the form:

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

where, a₁ = 5, b₁ = –7, c₁ = –5 and a₂ = 2, b₂ = k, c₂ = –1

Now, for the given system of equations to have a unique solution, we must have:

`(a_1)/(a_2) ≠ (b_1)/(b_2)`

⇒ `5/2 ≠ (-7)/k`

⇒ `k ≠ -14/5`

Hence, `k ≠ -14/5`.