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Question

For which value of k will the following pair of linear equations have no solution?
3x+y=1
(2k1)x+(k1)y=2k+1

A
k=4
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B
k=1
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C
k=2
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D
k=5
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Solution

The correct option is C k=2

The given pair of equations are:
3x+y=1...(1)
(2k1)x+(k1)y=2k+1..(2)
Now rearranging eq1 and eq2 will get
3x+y1=0...(3)
(2k1)x+(k1)y(2k+1)=0..(4)
Now compare with
a1=3,b1=1,c1=1
a2=2k1,b2=k1,c2=(2k+1)
Now we get
a1a2=32k1,b1b2=1k1,c1c2=1(2k+1)
Now will take
a1a2=b1b2
32k1=1k1
3k3=2k1
3k2k=1+3
k=2
Hence k=2 is the value.


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