Ex 3.1

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

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### Transcript

Ex 3.1, 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 2x + y – 6 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 2 , b1 = 1 , c1 = –6 4x – 2y – 4 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 4 , b2 = –2 , c2 = –4 a1 = 2 , b1 = 1 , c1 = –6 & a2 = 4 , b2 = –2 , c2 = –4 𝒂𝟏/𝒂𝟐 𝑎1/𝑎2 = 2/4 𝑎1/𝑎2 = 1/2 𝒃𝟏/𝒃𝟐 𝑏1/𝑏2 = 1/(−2) 𝑏1/𝑏2 = (−1)/2 𝒄𝟏/𝒄𝟐 𝑐1/𝑐2 = (−6)/(−4) 𝑐1/𝑐2 = 3/2 Since 𝑎1/𝑎2 ≠ 𝑏1/𝑏2 We have a unique solution Therefore, our system is consistent For Equation (1) 2x + y = 6 Putting x = 0 2(0) + y = 6 0 + y = 6 y = 6 So, x = 0, y = 6 is a solution i.e. (0, 6) is a solution Putting y = 0 2x + 0 = 6 2x = 6 x = 6/2 x = 3 So, x = 3, y = 0 is a solution i.e. (3, 0) is a solution For Equation (2) 4x − 2y = 4 Putting x = 0 4(0) − 2y = 4 0 − 2y = 4 −2y = 4 y = 4/(−2) y = −2 So, x = 0, y = −2 is a solution i.e. (0, −2) is a solution Putting y = 0 4x − 2(0) = 4 4x − 0 = 4 4x = 4 x = 4/4 x = 1 So, x = 1, y = 0 is a solution i.e. (1, 0) is a solution We will plot both equations on the graph So, (2, 2) is the solution

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.