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Question 2 The value of k for which the system of equations 3π‘₯βˆ’π‘˜π‘¦=7 and 6π‘₯+10𝑦=3 is inconsistent, is (A) – 10 (B) -5 (C) 5 (D) 7Since the system of equations is inconsistent It has no solution Finding ratios πŸ‘π’™βˆ’π’Œπ’šβˆ’πŸ•=𝟎 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 3 , b1 = βˆ’k , c1 = βˆ’7 πŸ”π’™+πŸπŸŽπ’šβˆ’πŸ‘=𝟎 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 6 , b2 = 10, c2 = βˆ’3 π’‚πŸ/π’‚πŸ π‘Ž1/π‘Ž2 = 3/6 π‘Ž1/π‘Ž2 = 1/2 π’ƒπŸ/π’ƒπŸ 𝑏1/𝑏2 = (βˆ’π‘˜)/10 π’„πŸ/π’„πŸ 𝑐1/𝑐2 = (βˆ’7)/(βˆ’3) 𝑐1/𝑐2 = 7/3 Since the equations don’t have a solution π‘Ž1/π‘Ž2 = 𝑏1/𝑏2 β‰  𝑐1/𝑐2 1/2=(βˆ’π‘˜)/10β‰ 7/3 Thus, 1/2=(βˆ’π‘˜)/10 10/2=βˆ’π‘˜ 5 = βˆ’k βˆ’5 = k k = βˆ’5 So, the correct answer is (B)

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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 and Computer Science at Teachoo