# Ex 3.2, 4 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 3.2,4 Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically x + y = 5, 2x + 2y = 10 x + y = 5 2x + 2y = 10 ∴ a1 = 1 , b1 = 1 , c1 = –5 & a2 = 2 , b2 = 2 , c2 = –10 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 = 𝑐1/𝑐2 We have infinitely many solutions Therefore, our system is consistent. Now we solve our equations graphically Solving (1) x + y – 5 = 0 y = 5 − x Solving (2) 2x + 2y – 10 = 0 2y = 10 − 2x y = (10 − 2𝑥)/2 Ex 3.2,4 Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically (ii) x – y = 8, 3x – 3y = 16 x – y = 8 3x – 3y = 16 ∴ a1 = 1 , b1 = –1 , c1 = –8 & a2 = 3 , b2 = –3 , c2 = –16 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 ≠ 𝑐1/𝑐2 We have no solution. Therefore, our system is inconsistent. Ex 3.2,4 Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically (iii) 2x + y – 6 = 0 , 4x – 2y – 4 = 0 2x + y – 6 = 0 4x – 2y – 4 = 0 a1 = 2 , b1 = 1 , c1 = –6 & a2 = 4 , b2 = –2 , c2 = –4 Since 𝑎1/𝑎2 ≠ 𝑏1/𝑏2 We have a unique solution. Therefore, our system is consistent. Solving (1) 2x + y – 6 = 0 y = 6 − 2x Solving (2) 4x − 2y – 4 = 0 2y = 4x – 4 y = (4𝑥 − 4)/2 Ex 3.2,4 Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically (iv) 2x – 2y – 4 = 0, 4x – 4y – 5 = 0 2x – 2y – 4 = 0 4x – 4y – 5 = 0 a1 = 2 , b1 = 1 , c1 = –6 a2 = 4 , b2 = –4 , c2 = –5 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 ≠ 𝑐1/𝑐2 We have no solution. Therefore, our system is inconsistent.

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.