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For what value of 'k' will …

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For what value of 'k' will the following system of linear equations has no solution? 3x + y = 1 (2k – 1)x + (k – 1)y = 2k + 1.

Posted by Cheshta Garg 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Shubham Sinha 4 months ago

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 get 3x + y − 1 = 0 ........... (3) (2k−1)x + (k−1)y − (2k+1) = 0 ........ (4) Now compare with a1 = 3, b1 = 1, c1 = −1 a2 = 2k−1, b2 = k−1, c2 = −(2k+1) Now we get a1a2 = 32k−1 , b1b2 = 1k−1 , c1c2 = −1−(2k+1) Now will take a1a2 = b1b2 ⇒32k−1 = 1k−1 ⇒3k−3 = 2k−1 ⇒3k−2k = −1+3 ⇒k = 2 Hence k = 2 is the value.

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