Ex 3.2, 3 - On comparing ratios, find if consistent or inconsistent

Ex 3.2, 3 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2

 

  1. Class 10
  2. Important Questions for Exam - Class 10

Transcript

Ex 3.2, 3 On comparing the ratios ๐‘Ž1/๐‘Ž2 , ๐‘1/๐‘2 & ๐‘1/๐‘2 , find out whether the following pair of linear equations are consistent, or inconsistent. 3x + 2y = 5 ; 2x โ€“ 3y = 7 3x + 2y โ€“ 5 = 0 2x โ€“ 3y โ€“ 7 = 0 3x + 2y โ€“ 5 = 0 Comparing with a1x + b1y + c1 = 0 โˆด a1 = 3 , b1 = 2 , c1 = โ€“5 2x โ€“ 3y โ€“ 7 = 0 Comparing with a2x + b2y + c2 = 0 โˆด a2 = 2 , b2 = โ€“3 , c2 = โ€“7 a1 = 3 , b1 = 2 , c1 = โ€“5 & a2 = 2 , b2 = โ€“3 , c2 = โ€“7 ๐’‚๐Ÿ/๐’‚๐Ÿ ๐‘Ž1/๐‘Ž2 = 3/2 ๐’ƒ๐Ÿ/๐’ƒ๐Ÿ ๐‘1/๐‘2 = 2/(โˆ’3) ๐‘1/๐‘2 = (โˆ’2)/3 ๐’„๐Ÿ/๐’„๐Ÿ ๐‘1/๐‘2 = (โˆ’5)/(โˆ’7) ๐‘1/๐‘2 = 5/7 Since ๐‘Ž1/๐‘Ž2 โ‰  ๐‘1/๐‘2 We have a unique solution Therefore, our system is consistent.

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
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.