Question

For what value of k the following system of equations has a unique solutions :

x - ky = 2

3x + 2y = -5

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Answer 1

Answer:

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Answer 2

The given system of equations can be written as

x - ky - 2 = 0

3x + 2y + 5 = 0

The given system of equation is the form

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Where,

a1 = 1 , b1 = -k, c1 = -2

a2 = 3, b2 = 2 ,c2 = 5

clearly,

For unique solutions a1/a2 is not equal to b1/b2.

⇒ 1/3 is not equal to -k/2

⇒ k is not equal to-2/3

Hence, k can be take any value except-2/3