Ex 3.5, 1 - Which pair has unique, no solution or infinitely - Ex 3.5

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

Transcript

Ex 3.5 ,1 Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method x – 3y – 3 = 0 3x – 9y – 2 = 0 x – 3y – 3 = 0 3x – 9y – 2 = 0 a1 = 1 , b1 = –3 , c1 = –3 & a2 = 3 , b2 = –9 , c2 = –2 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 ≠ 𝑐1/𝑐2 We have no solution. Ex 3.5 ,1 Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method (ii) 2x + y = 5 3x + 2y = 8 2x + y = 5 3x + 2y = 8 a1 = 2 , b1 = 1 , c1 = –5 & a2 = 3 , b2 = –9 , c2 = –2 Since 𝑎1/𝑎2 ≠ 𝑏1/𝑏2 We have a unique solution Solving 2x + y = 5 …(1) 3x + 2y = 8 …(2) For cross-multiplication 2x + y – 5 = 0 3x + 2y – 8 = 0 Now, 𝑥/2 = 1/1 x = 2 × 1 ∴ x = 2 Therefore, x = 2 , y = 1 is the solution of our equation Ex 3.5 ,1 Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method (iii) 3x – 5y = 20 6x – 10y = 40 3x – 5y = 20 6x – 10y = 40 a1 = 3 , b1 = –5 , c1 = –20 & a2 = 6 , b2 = –10 , c2 = –40 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 = 𝑐1/𝑐2 We have infinitely many solutions Ex 3.5 ,1 Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method (iv) x – 3y – 7 = 0 3x – 3y – 15 = 0 x – 3y – 7 = 0 3x – 3y – 15 = 0 a1 = 1 , b1 = –3 , c1 = –7 & a2 = 3 , b2 = –3 , c2 = –15 Since 𝑎1/𝑎2 ≠ 𝑏1/𝑏2 We have a unique solution Solving x – 3y – 7 = 0 …(1) 3x – 3y – 15 = 0 …(2) Using cross-multiplication Now, 𝑥/24 = 1/6 x = 24/6 ∴ x = 4 Therefore, x = 4 , y = –1 is the solution of our equation

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.