Question

If the system of linear equations x - ky = 2 and 3x + 2y = -5 has unique solution, then the value of k is __________ .

Answer 1

hey frnd

the solution is in the pic.

refer it

hope it helps u..!!

Answer 2

Given that,

The system of equations x - ky = 2 and 3x + 2y = -5 has unique solution.

To find,

The value of k.

Solution,

If the system of equations have unique solutions, it would mean that :

$\dfrac{a_1}{a_2}\ne \dfrac{b_1}{b_2}\ne \dfrac{c_1}{c_2}$

Here,

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

So,

$\dfrac{1}{3}\ne \dfrac{-k}{2}\\\\k\ne \dfrac{-2}{3}$

So, k can take any value except $\dfrac{-2}{3}$. Hence, this is the required solution.