Sunday 31 March 2013

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

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