Find the value of k for which the system of equations have infinitely manysolutions
x - ky = 2, 3x+ 6y = -5.

Given equations
x − ky = 2
3x+ 6y = −5

We know that the most general form of a pair of linear equations is a ₁ x + b ₁ y + c ₁ = 0 and a ₂ x + b ₂ y + c ₂ = 0 where a ₁ , a ₂ , b ₁ , b ₂ , c ₁ , c ₂ are real numbers, such that a ₁ ² + b ₁ ² ≠ 0; a ₂ ² + b ₂ ² ≠ 0. So, a ₁ = 1, b ₁ = - k, c ₁ = -2 and a ₂ = 3, b ₂ = 6, c = 5
Given, the system of equations have infinitely many solutions
∴

So,

Let us consider
Then, we get k = -6/3 = -2

Next, consider

Then, we get k = 12/5

Ans. The value of k = -2 or 12/5