web analytics

Ex 3.2, 2 - On comparing the ratios a1/a2, b1/b2,  c1/c2 - Finding ratios (Consistency)

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

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 โˆด a1 = 5 , b1 = โˆ’ 4 , c1 = 8 & a2 = 7x , b2 = 6 , c2 = 9 Since ๐‘Ž1/๐‘Ž2 โ‰  ๐‘1/๐‘2 We have a 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 โˆด a1 = 9 , b1 = 3 , c1 = 12 & a2 = 18 , b2 = 6 , c2 = 24 Since ๐‘Ž1/๐‘Ž2 = ๐‘1/๐‘2 = ๐‘1/๐‘2 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 โˆด a1 = 6 , b1 = 3 , c1 = 10 & a2 = 2 , b2 = โˆ’ 1 , c2 = 9 Since ๐‘Ž1/๐‘Ž2 = ๐‘1/๐‘2 โ‰  ๐‘1/๐‘2 We have no solution. Therefore, the lines represent the linear equations are parallel

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail