If the system of equations 3x + y = 1 and (2k – 1)x + (k – 1)y = 2k + 1

 is inconsistent, then k =

(a) -1   (b) 0  (c) 1  (d) 2

 

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Given equations 3x + y = 1 (2k – 1)x + (k – 1)y = 2k + 1 Now, Since equations are inconsistent It means that the lines are parallel 𝑎1/𝑎2 = 𝑏1/𝑏2 ≠ 𝑐1/𝑐2 𝟑/((𝟐𝒌 − 𝟏)) = 𝟏/((𝒌 − 𝟏)) ≠ 𝟏/((𝟐𝒌 + 𝟏)) Thus, 𝟑/((𝟐𝒌 − 𝟏)) = 𝟏/((𝒌 − 𝟏)) 3(k − 1) = (2k − 1) 3k − 3 = 2k − 1 3k − 2k = −1 + 3 k = 2 So, the correct answer is (d)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.