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Cross Multiplication Method

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Chapter 3 Class 10 Pair of Linear Equations in Two Variables

Serial order wise

Last updated at May 29, 2023 by Teachoo

Ex 3.5 ,1 Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method (iii) 3x – 5y = 20 6x – 10y = 40 3x – 5y = 20 6x – 10y = 40 3x – 5y = 20 3x – 5y – 20 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 3,b1 = –5,c1 = –20 6x – 10y = 40 6x – 10y – 40 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 6,b2 = –10,c2 = –40 a1 = 3, b1 = –5, c1 = –20 & a2 = 6, b2 = –10, c2 = –40 𝒂𝟏/𝒂𝟐 𝑎1/𝑎2 = 3/6 𝑎1/𝑎2 = 1/2 𝒃𝟏/𝒃𝟐 𝑏1/𝑏2 = (−5)/(−10) 𝑏1/𝑏2 = 1/2 𝒄𝟏/𝒄𝟐 𝑐1/𝑐2 = (−20)/(−40) 𝑐1/𝑐2 = 1/2 Since 𝒂𝟏/𝒂𝟐 = 𝒃𝟏/𝒃𝟐 = 𝒄𝟏/𝒄𝟐 We have infinitely many solutions