Ex 3.5, 2 (i) For which values of a and b does the pair - Ex 3.5

Ex 3.5, 2 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Ex 3.5, 2 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3 Ex 3.5, 2 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 4

 

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 2 (i) For which values of a and b does the following pair of linear equations have an infinite number of solutions? 2x+ 3y = 7 (a – b) x + (a + b) y= 3a + b – 2 2x + 3y = 7 (a – b)x + (a + b) y = 3a + b – 2 2x + 3y = 7 2x + 3y – 7 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 2,b1 = 3,c1 = –7 (a – b)x + (a + b)y = 3a + b – 2 (a – b)x + (a + b)y – (3a + b – 2)= 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = (a – b),b2 = (a + b), c2 = – (3a + b – 2) So, a1 = 2, b1 = 3, c1 = –7 & a2 = (a – b), b2 = (a + b), c2 = – (3a + b – 2) It is given that the equation has infinite number of solutions So, 𝒂𝟏/𝒂𝟐 = 𝒃𝟏/𝒃𝟐 = 𝒄𝟏/𝒄𝟐 Putting in values 2/((𝑎 − 𝑏)) = 3/((𝑎 + 𝑏)) = (−7)/(−(3𝑎 + 𝑏 − 2)) 𝟐/((𝒂 − 𝒃)) = 𝟑/((𝒂 + 𝒃)) = (−𝟕)/(−(𝟑𝒂 + 𝒃 − 𝟐)) Solving 𝟐/((𝒂 − 𝒃)) = 𝟑/((𝒂 + 𝒃)) 2(a + b) = 3(a – b) 2a + 2b = 3a – 3b 2b + 3b = 3a – 2a 5b = a a = 5b Solving 𝟐/((𝒂 − 𝒃)) = 𝟕/((𝟑𝒂 + 𝒃 − 𝟐)) 2(3a + b – 2) = 7(a - b) 6a + 2b – 4 = 7a – 7b 2b – 4 + 7b = 7a – 6a 9b – 4 = a Comparing (3) and (4) 5b = 9b – 4 4 = 9b – 5b 4 = 4b 4b = 4 b = 𝟒/𝟒 = 1 Putting b = 1 in (3) a = 5b a = 5(1) a = 5 Therefore, for a = 5, b = 1 the given set of equations have infinitely many solutions

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.