Learn all Concepts of Chapter 3 Class 10 (with VIDEOS). Check - Linear Equations in 2 Variables - Class 10

Last updated at Dec. 18, 2020 by Teachoo

Learn all Concepts of Chapter 3 Class 10 (with VIDEOS). Check - Linear Equations in 2 Variables - Class 10

Transcript

Ex 3.2, 2 On comparing the ratios ๐1/๐2 , ๐1/๐2 & ๐1/๐2 , find out whether the lines representing the following pair of linear equations intersect at a point, parallel or coincident 5x โ 4y + 8 = 0 ; 7x + 6y โ 9 = 0 5x โ 4y + 8 = 0 7x + 6y โ 9 = 0 5x โ 4y + 8 = 0 Comparing with a1x + b1y + c1 = 0 โด a1 = 5 , b1 = โ4 , c1 = 8 7x + 6y โ 9 = 0 Comparing with a2x + b2y + c2 = 0 โด a2 = 7 , b2 = 6 , c2 = โ9 โด a1 = 5 , b1 = โ4 , c1 = 8 & a2 = 7 , b2 = 6 , c2 = โ9 ๐๐/๐๐ ๐1/๐2 = 5/7 ๐๐/๐๐ ๐1/๐2 = (โ4)/6 ๐1/๐2 = (โ2)/3 ๐๐/๐๐ ๐1/๐2 = 8/(โ9) ๐1/๐2 = (โ8)/9 Since ๐1/๐2 โ ๐1/๐2 So, have unique solution Therefore, the lines that represent the linear equations intersect at a point Ex 3.2, 2 On comparing the ratios ๐1/๐2 , ๐1/๐2 & ๐1/๐2 , 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 โด a1 = 9 , b1 = 3 , c1 = 12 18x + 6y + 24 = 0 Comparing with a2x + b2y + c2 = 0 โด a2 = 18 , b2 = 6 , c2 = 24 โด a1 = 9 , b1 = 3 , c1 = 12 & a2 = 18 , b2 = 6 , c2 = 24 ๐๐/๐๐ ๐1/๐2 = 9/18 ๐1/๐2 = 1/2 ๐๐/๐๐ ๐1/๐2 = 3/6 ๐1/๐2 = 1/2 ๐๐/๐๐ ๐1/๐2 = 12/24 ๐1/๐2 = 1/2 Since ๐1/๐2 = ๐1/๐2 = ๐1/๐2 So, we have infinite solutions Therefore, the lines that represent the linear equations are coincident Ex 3.2, 2 On comparing the ratios ๐1/๐2 , ๐1/๐2 & ๐1/๐2 , find out whether the lines representing the following pair of linear equations intersect at a point, parallel or coincident (iii) 6x โ 3y + 10 = 0 ; 2x โ y + 9 = 0 6x โ 3y + 10 = 0 2x โ y + 9 = 0 6x โ 3y + 10 = 0 Comparing with a1x + b1y + c1 = 0 โด a1 = 6 , b1 = โ3 , c1 = 10 2x โ y + 9 = 0 Comparing with a2x + b2y + c2 = 0 โด a2 = 2 , b2 = โ1 , c2 = 9 โด a1 = 6 , b1 = โ3 , c1 = 10 & a2 = 2 , b2 = โ1 , c2 = 9 ๐๐/๐๐ ๐1/๐2 = 6/2 ๐1/๐2 = 3 ๐๐/๐๐ ๐1/๐2 = (โ3)/(โ1) ๐1/๐2 = 3 ๐๐/๐๐ ๐1/๐2 = 10/9 Since ๐1/๐2 = ๐1/๐2 โ ๐1/๐2 So, we have no solution Therefore, the lines represent the linear equations are parallel

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.