# Ex 3.2, 3

Last updated at Dec. 28, 2018 by Teachoo

Last updated at Dec. 28, 2018 by Teachoo

Transcript

Ex 3.2,3 On comparing the ratios ๐1/๐2 , ๐1/๐2 & ๐1/๐2 , 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 3x + 2y โ 5 = 0 Comparing with a1x + b1y + c1 = 0 โด a1 = 3 , b1 = 2 , c1 = โ5 2x โ 3y โ 7 = 0 Comparing with a2x + b2y + c2 = 0 โด a2 = 2 , b2 = โ3 , c2 = โ7 a1 = 3 , b1 = 2 , c1 = โ5 & a2 = 2 , b2 = โ3 , c2 = โ7 Since ๐1/๐2 โ ๐1/๐2 We have a unique solution Therefore, our system is consistent. Ex 3.2,3 On comparing the ratios ๐1/๐2 , ๐1/๐2 & ๐1/๐2 , find out whether the following pair of linear equations are consistent, or inconsistent. (ii) 2x -3y = 8 ; 4x - 6y = 9 2x โ 3y โ 8 = 0 4x โ 6y โ 9 = 0 2x โ 3y โ 8 = 0 Comparing with a1x + b1y + c1 = 0 โด a1 = 2 , b1 = โ 3 , c1 = โ 8 4x โ 6y โ 9 = 0 Comparing with a2x + b2y + c2 = 0 โด a2 = 4 , b2 = โ 6 , c2 = โ 9 โด a1 = 2, b1 = โ 3 , c1 = โ 8 a2 = 4, b2 = โ6, c2 = โ 9 Since ๐1/๐2 = ๐1/๐2 โ ๐1/๐2 We have no solution. Therefore, our system is inconsistent. Ex 3.2,3 On comparing the ratios ๐1/๐2 , ๐1/๐2 & ๐1/๐2 , find out whether the following pair of linear equations are consistent, or inconsistent. (iii) 3/2x + 5/3y = 7 ; 9x - 10y = 14 3/2 ๐ฅ + 5/3 ๐ฆ โ 7 =0 9x โ 10y โ 14 = 0 ๐/๐ ๐ + ๐/๐ ๐ โ ๐ =๐ Comparing with a1x + b1y + c1 = 0 โด a1 = 3/2 , b1 = 5/3 , c1 = โ 7 9x โ 10y โ 14 = 0 Comparing with a2x + b2y + c2 = 0 โด a2 = 9 , b2 = โ 10, c2 = โ 14 โด a1 = 3/2 , b1 = 5/3 , c1 = โ 7 & a2 = 9 , b2 = โ 10, c2 = โ 14 ๐๐/๐๐ ๐1/๐2 = (3/2)/9 ๐1/๐2 = 3/(2 ร 9) ๐1/๐2 = 1/(2 ร3) ๐1/๐2 = 1/6 ๐๐/๐๐ ๐1/๐2 = (5/3)/10 ๐1/๐2 = 5/(3 ร10) ๐1/๐2 = 1/(3 ร 2) ๐1/๐2 = 1/6 ๐๐/๐๐ ๐1/๐2 = (โ7)/(โ14) ๐1/๐2 = 1/2 Since ๐1/๐2 = ๐1/๐2 โ ๐1/๐2 We have no solution. Therefore, our system is inconsistent. Note: This answer does not match the book answer. If we are wrong, please comment below

Chapter 3 Class 10 Pair of Linear Equations in Two Variables

Example 6
Important

Example 10 Important

Example 11 Important

Example 13 Important

Example 14 Important

Example 19 Important

Ex 3.2, 1 Important

Ex 3.2, 3 Important You are here

Ex 3.2, 6 Important

Ex 3.2, 7 Important

Ex 3.5, 2 Important

Ex 3.6, 1 (i) and (ii) Important

Ex 3.6, 1 (iii) and (iv) Important

Ex 3.6, 1 (v) and (vi) Important

Ex 3.6, 1 (vii) and (viii) Important

Ex 3.6, 2 Important

Class 10

Important Questions for Exam - Class 10

- Chapter 1 Class 10 Real Numbers
- Chapter 2 Class 10 Polynomials
- Chapter 3 Class 10 Pair of Linear Equations in Two Variables
- Chapter 4 Class 10 Quadratic Equations
- Chapter 5 Class 10 Arithmetic Progressions
- Chapter 6 Class 10 Triangles
- Chapter 7 Class 10 Coordinate Geometry
- Chapter 8 Class 10 Introduction to Trignometry
- Chapter 9 Class 10 Some Applications of Trignometry
- Chapter 10 Class 10 Circles
- Chapter 11 Class 10 Constructions
- Chapter 12 Class 10 Areas related to Circles
- Chapter 13 Class 10 Surface Areas and Volumes
- Chapter 14 Class 10 Statistics
- Chapter 15 Class 10 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.