web analytics

Ex 3.2, 3 - On comparing ratios, find whether consistent - Ex 3.2

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

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 ; 2xโ€“ 3y= 7 3x + 2y โ€“ 5 = 0 2x โ€“ 3y โ€“ 7 = 0 a1 = 3 , b1 = 2 , c1 = โ€“5 & a2 = 2 , b2 = โ€“3 , c2 = โ€“7 Since ๐‘Ž1/๐‘Ž2 โ‰  ๐‘1/๐‘2 We have a unique solution Therefore, our system is consistent. 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. (ii) 2x -3y = 8 ; 4x - 6y = 9 2x โ€“ 3y โˆ’ 8 = 0 4x โ€“ 6y โ€“ 9 = 0 โˆด a1 = 2, b1 = โˆ’ 3 , c1 = โˆ’ 8 a2 = 4, b2 = โˆ’6, c2 = โˆ’ 9 Since ๐‘Ž1/๐‘Ž2 = ๐‘1/๐‘2 โ‰  ๐‘1/๐‘2 We have no solution. Therefore, our system is inconsistent. 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. (iii) 3/2x + 5/3y = 7 ; 9x - 10y = 14 3/2 ๐‘ฅ + 5/3 ๐‘ฆ โ€“ 7 =0 9x โ€“ 10y โ€“ 14 = 0 โˆด a1 = 3/2 , b1 = 5/3 , c1 = โ€“ 7 & a2 = 9 , b2 = โ€“ 10, c2 = โ€“ 14 Since ๐‘Ž1/๐‘Ž2 = ๐‘1/๐‘2 โ‰  ๐‘1/๐‘2 We have no solution. Therefore, our system is inconsistent. Ex3.2,3 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. (iv) 5x โ€“ 3y = 11 , -10x + 6y = -22 5x โ€“ 3y โ€“ 11 = 0 โˆ’10x + 6y + 22 = 0 โˆด a1 = 5 , b1 = โˆ’3 , c1 = โ€“ 11 & a2 = โˆ’ 10 , b2 = 6, c2 = 22 Since ๐‘Ž1/๐‘Ž2 = ๐‘1/๐‘2 = ๐‘1/๐‘2 We have infinitely many solutions Therefore, our system is consistent. Now we solve our equations graphically 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. (v) 4/3 x + 2y = 8 ; 2x + 3y = 12 4/3 x + 2y โ€“ 8 = 0 2x + 3y โ€“ 12 = 0 โˆด a1 = 4/3 , b1 = 2 , c1 = โ€“ 8 & a2 = 2, b2 = 3 c2 = โˆ’12 Since ๐‘Ž1/๐‘Ž2 = ๐‘1/๐‘2 = ๐‘1/๐‘2 We have infinite solutions. Therefore, our system is consistent.

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