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

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  1. Chapter 3 Class 10 Pair of Linear Equations in Two Variables
  2. Serial order wise

Transcript

Ex 3.2, 2 On comparing the ratios ๐‘Ž1/๐‘Ž2 , ๐‘1/๐‘2 & ๐‘1/๐‘2 , 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 โˆด a1 = 5 , b1 = โˆ’4 , c1 = 8 7x + 6y โ€“ 9 = 0 Comparing with a2x + b2y + c2 = 0 โˆด a2 = 7 , b2 = 6 , c2 = โˆ’9 โˆด a1 = 5 , b1 = โˆ’4 , c1 = 8 & a2 = 7 , b2 = 6 , c2 = โˆ’9 ๐’‚๐Ÿ/๐’‚๐Ÿ ๐‘Ž1/๐‘Ž2 = 5/7 ๐’ƒ๐Ÿ/๐’ƒ๐Ÿ ๐‘1/๐‘2 = (โˆ’4)/6 ๐‘1/๐‘2 = (โˆ’2)/3 ๐’„๐Ÿ/๐’„๐Ÿ ๐‘1/๐‘2 = 8/(โˆ’9) ๐‘1/๐‘2 = (โˆ’8)/9 Since ๐‘Ž1/๐‘Ž2 โ‰  ๐‘1/๐‘2 So, have unique solution Therefore, the lines that represent the linear equations intersect at a point Ex 3.2, 2 On comparing the ratios ๐‘Ž1/๐‘Ž2 , ๐‘1/๐‘2 & ๐‘1/๐‘2 , 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 โˆด a1 = 9 , b1 = 3 , c1 = 12 18x + 6y + 24 = 0 Comparing with a2x + b2y + c2 = 0 โˆด a2 = 18 , b2 = 6 , c2 = 24 โˆด a1 = 9 , b1 = 3 , c1 = 12 & a2 = 18 , b2 = 6 , c2 = 24 ๐’‚๐Ÿ/๐’‚๐Ÿ ๐‘Ž1/๐‘Ž2 = 9/18 ๐‘Ž1/๐‘Ž2 = 1/2 ๐’ƒ๐Ÿ/๐’ƒ๐Ÿ ๐‘1/๐‘2 = 3/6 ๐‘1/๐‘2 = 1/2 ๐’„๐Ÿ/๐’„๐Ÿ ๐‘1/๐‘2 = 12/24 ๐‘1/๐‘2 = 1/2 Since ๐‘Ž1/๐‘Ž2 = ๐‘1/๐‘2 = ๐‘1/๐‘2 So, we have infinite solutions Therefore, the lines that represent the linear equations are coincident Ex 3.2, 2 On comparing the ratios ๐‘Ž1/๐‘Ž2 , ๐‘1/๐‘2 & ๐‘1/๐‘2 , 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 โˆด a1 = 6 , b1 = โˆ’3 , c1 = 10 2x โ€“ y + 9 = 0 Comparing with a2x + b2y + c2 = 0 โˆด a2 = 2 , b2 = โˆ’1 , c2 = 9 โˆด a1 = 6 , b1 = โˆ’3 , c1 = 10 & a2 = 2 , b2 = โˆ’1 , c2 = 9 ๐’‚๐Ÿ/๐’‚๐Ÿ ๐‘Ž1/๐‘Ž2 = 6/2 ๐‘Ž1/๐‘Ž2 = 3 ๐’ƒ๐Ÿ/๐’ƒ๐Ÿ ๐‘1/๐‘2 = (โˆ’3)/(โˆ’1) ๐‘1/๐‘2 = 3 ๐’„๐Ÿ/๐’„๐Ÿ ๐‘1/๐‘2 = 10/9 Since ๐‘Ž1/๐‘Ž2 = ๐‘1/๐‘2 โ‰  ๐‘1/๐‘2 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.