Question

Find the values of k so that the pair of linear equations kx - 2y = 3 And 3x + y = 5 has a unique solution

Answer 1

unique solution means we can say that lines are intersecting at 1 point so, we know
a1/a2 does not equal to b1/b2
k/3=-2/1
k=-6
so k can be any number except -6
I HOPE THIS WILL HELP U

Answer 2

Answer:

Step-by-step explanation:

A unique solution means these two lines intersect at a point.

It means they have a common point.

Now we can solve these simultaneously.

Kx - 2y = 3...........1)

3x + y = 5............... 2)

We can eliminate y.

We multiply equation 2 by 2 then add equation 1.

We have :

6x + kx = 18

x(6 + k) = 18

x = 18/(6 + k)

Substitute this in 2:

54/(6 + k) + y = 5

y = 5 - 54/(6 + k)

Replace this in 1:

18k/(6 + k) - 10 + 108/(6 + k) = 5

Multiply through by (6 + k)

18k - 10(6 + k) + 108 = 5(6 + k)

18k - 60 - 10k + 108 = 30 + 5k

18k - 10k - 5k = 30 + 60 - 108

3k = - 18

k = - 18/3

k = - 6