# Ex 3.2, 3 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

Last updated at Dec. 28, 2018 by Teachoo

Last updated at Dec. 28, 2018 by Teachoo

Transcript

Ex 3.2,3 On comparing the ratios ๐1/๐2 , ๐1/๐2 & ๐1/๐2 , find out whether the following pair of linear equations are consistent, or inconsistent. 3x+ 2y= 5 ; 2xโ 3y= 7 3x + 2y โ 5 = 0 2x โ 3y โ 7 = 0 3x + 2y โ 5 = 0 Comparing with a1x + b1y + c1 = 0 โด a1 = 3 , b1 = 2 , c1 = โ5 2x โ 3y โ 7 = 0 Comparing with a2x + b2y + c2 = 0 โด a2 = 2 , b2 = โ3 , c2 = โ7 a1 = 3 , b1 = 2 , c1 = โ5 & a2 = 2 , b2 = โ3 , c2 = โ7 Since ๐1/๐2 โ ๐1/๐2 We have a unique solution Therefore, our system is consistent. Ex 3.2,3 On comparing the ratios ๐1/๐2 , ๐1/๐2 & ๐1/๐2 , find out whether the following pair of linear equations are consistent, or inconsistent. (ii) 2x -3y = 8 ; 4x - 6y = 9 2x โ 3y โ 8 = 0 4x โ 6y โ 9 = 0 2x โ 3y โ 8 = 0 Comparing with a1x + b1y + c1 = 0 โด a1 = 2 , b1 = โ 3 , c1 = โ 8 4x โ 6y โ 9 = 0 Comparing with a2x + b2y + c2 = 0 โด a2 = 4 , b2 = โ 6 , c2 = โ 9 โด a1 = 2, b1 = โ 3 , c1 = โ 8 a2 = 4, b2 = โ6, c2 = โ 9 Since ๐1/๐2 = ๐1/๐2 โ ๐1/๐2 We have no solution. Therefore, our system is inconsistent. Ex 3.2,3 On comparing the ratios ๐1/๐2 , ๐1/๐2 & ๐1/๐2 , find out whether the following pair of linear equations are consistent, or inconsistent. (iii) 3/2x + 5/3y = 7 ; 9x - 10y = 14 3/2 ๐ฅ + 5/3 ๐ฆ โ 7 =0 9x โ 10y โ 14 = 0 ๐/๐ ๐ + ๐/๐ ๐ โ ๐ =๐ Comparing with a1x + b1y + c1 = 0 โด a1 = 3/2 , b1 = 5/3 , c1 = โ 7 9x โ 10y โ 14 = 0 Comparing with a2x + b2y + c2 = 0 โด a2 = 9 , b2 = โ 10, c2 = โ 14 โด a1 = 3/2 , b1 = 5/3 , c1 = โ 7 & a2 = 9 , b2 = โ 10, c2 = โ 14 ๐๐/๐๐ ๐1/๐2 = (3/2)/9 ๐1/๐2 = 3/(2 ร 9) ๐1/๐2 = 1/(2 ร3) ๐1/๐2 = 1/6 ๐๐/๐๐ ๐1/๐2 = (5/3)/10 ๐1/๐2 = 5/(3 ร10) ๐1/๐2 = 1/(3 ร 2) ๐1/๐2 = 1/6 ๐๐/๐๐ ๐1/๐2 = (โ7)/(โ14) ๐1/๐2 = 1/2 Since ๐1/๐2 = ๐1/๐2 โ ๐1/๐2 We have no solution. Therefore, our system is inconsistent. Note: This answer does not match the book answer. If we are wrong, please comment below

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.