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Question

For which value of k will the following pair of linear equations have no solution?3x+y=1(2kâˆ’1)x+(kâˆ’1)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)(2k−1)x+(k−1)y=2k+1..(2)Now rearranging eq1 and eq2 will get3x+y−1=0...(3)(2k−1)x+(k−1)y−(2k+1)=0..(4)Now compare witha1=3,b1=1,c1=−1a2=2k−1,b2=k−1,c2=−(2k+1)Now we geta1a2=32k−1,b1b2=1k−1,c1c2=−1−(2k+1)Now will takea1a2=b1b2⇒32k−1=1k−1⇒3k−3=2k−1⇒3k−2k=−1+3⇒k=2Hence k=2 is the value.

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