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Ex 3.1, 2 On comparing the ratios 𝑎1/𝑎2 , 𝑏1/𝑏2 & 𝑐1/𝑐2 , find out whether the lines representing the following pair of linear equations intersect at a point, parallel or coincident (ii) 9x + 3y + 12 = 0 ; 18x + 6y + 24= 0 9x + 3y + 12 = 0 18x + 6y + 24 = 0 9x + 3y + 12 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 9 , b1 = 3 , c1 = 12 18x + 6y + 24 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 18 , b2 = 6 , c2 = 24 ∴ a1 = 9 , b1 = 3 , c1 = 12 & a2 = 18 , b2 = 6 , c2 = 24 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 = 𝑐1/𝑐2 So, we have infinite solutions Therefore, the lines that represent the linear equations are coincident

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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