For which value of k will the following pair of linear equations have no solution? 3x +y = 1 ; (2k –1) x + (k –1) y = 2k + 1

For which value of k will the following pair of linear equations have no solution?    

 3x +y = 1 ; (2k –1) x + (k –1) y = 2k + 1    

 3x +y = 1

Subtract 1 both side we get

3x + y – 1 = 0

 (2k –1) x + (k –1) y   = 2k + 1

Subtract 2k +1 both side we get

(2k –1) x + (k –1) y – (2k + 1)= 0

3x+y=1 and

(2k-1)x+(k-1)y=2k+1

They can be rewrite as:

3x + y - 1 = 0 and

(2k-1)x + (k-1)y - (2k+1) = 0 

 Compare with

We get 

And for no solution

Take

 

Cross multiply we get

 3k - 3 = 2k - 1

 k = 3-1

 k = 2

Hence Answer is k = 2