Question 2 (ii) - Cross Multiplication Method - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Ex 3.5, 2 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 5

Ex 3.5, 2 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 6
Ex 3.5, 2 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 7

Transcript

Ex 3.5 ,2 (ii) For which value of k will the following pair of linear equations have no solution? 3x + y = 1 (2k – 1) x + (k – 1) y = 2k+ 1 3x + y = 1 (2k – 1)x + (k – 1)y = 2k + 1 3x + y = 1 3x + y – 1 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 3, b1 = 1, c1 = –1 (2k – 1)x + (k – 1)y = 2k + 1 (2k – 1)x + (k – 1)y – (2k + 1)= 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = (2k – 1), b2 = (k – 1), c2 = – (2k + 1) So, a1 = 3, b1 = 1, c1 = –1 & a2 = (2k – 1), b2 = (k – 1), c2 = – (2k + 1) It is given that the equation has no solution So, 𝒂𝟏/𝒂𝟐 = 𝒃𝟏/𝒃𝟐 ≠ 𝒄𝟏/𝒄𝟐 Taking 𝒂𝟏/𝒂𝟐 = 𝒃𝟏/𝒃𝟐 3/((2𝑘 − 1)) = 1/((𝑘 − 1)) 3(k – 1) = 1(2k – 1) 3k – 3 = 2k – 1 3k – 2k = 3 – 1 k = 2 Therefore, for k = 2 the given set of equations have no solutions

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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.