Learn all Concepts of Chapter 3 Class 10 (with VIDEOS). Check - Linear Equations in 2 Variables - Class 10

Last updated at Dec. 18, 2020 by Teachoo

Learn all Concepts of Chapter 3 Class 10 (with VIDEOS). Check - Linear Equations in 2 Variables - Class 10

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 x + y = 5 x + y – 5 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 1 , b1 = 1 , c1 = –5 2x + 2y = 10 2x + 2y – 10 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 2 , b2 = 2 , c2 = –10 ∴ a1 = 1 , b1 = 1 , c1 = –5 & a2 = 2 , b2 = 2 , c2 = –10 𝒂𝟏/𝒂𝟐 𝑎1/𝑎2 = 1/2 𝒃𝟏/𝒃𝟐 𝑏1/𝑏2 = 1/2 𝒄𝟏/𝒄𝟐 𝑐1/𝑐2 = (−5)/(−10) 𝑐1/𝑐2 = 1/2 Since 𝑎1/𝑎2 = 𝑏1/𝑏2 = 𝑐1/𝑐2 We have infinitely many solutions Therefore, our system is consistent. Now we solve our equations graphically For Equation (1) x + y = 5 Putting x = 0 0 + y = 5 y = 5 So, x = 0, y = 5 is a solution i.e. (0, 5) is a solution Putting y = 0 x + 0 = 5 x = 5 So, x = 5, y = 0 is a solution i.e. (5, 0) is a solution For Equation (2) 2x + 2y = 10 Putting x = 0 2(0) + 2y = 10 0 + 2y = 10 2y = 10 y = 10/2 y = 5 So, x = 0, y = 5 is a solution i.e. (0, 5) is a solution Putting y = 0 2x + 2(0) = 10 2x + 0 = 10 2x = 10 x = 10/2 x = 5 So, x = 5, y = 0 is a solution i.e. (5, 0) is a solution We will plot both equations on the graph 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 x – y = 8 x – y – 8 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 1 , b1 = –1 , c1 = –8 3x – 3y = 16 3x – 3y – 16 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 3 , b2 = –3 , c2 = –16 ∴ a1 = 1 , b1 = –1 , c1 = –8 & a2 = 3 , b2 = –3 , c2 = –16 𝒂𝟏/𝒂𝟐 𝑎1/𝑎2 = 1/3 𝒃𝟏/𝒃𝟐 𝑏1/𝑏2 = (−1)/(−3) 𝑏1/𝑏2 = 1/3 𝒄𝟏/𝒄𝟐 𝑐1/𝑐2 = (−8)/(−16) 𝑐1/𝑐2 = 1/2 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 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 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 2x – 2y – 4 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 2 , b1 = −2 , c1 = –4 4x – 4y – 5 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 4 , b2 = –4 , c2 = –5 a1 = 2 , b1 = −2 , c1 = –4 a2 = 4 , b2 = –4 , c2 = –5 𝒂𝟏/𝒂𝟐 𝑎1/𝑎2 = 2/4 𝑎1/𝑎2 = 1/2 𝒃𝟏/𝒃𝟐 𝑏1/𝑏2 = (−2)/(−4) 𝑏1/𝑏2 = 1/2 𝒄𝟏/𝒄𝟐 𝑐1/𝑐2 = (−2)/(−5) 𝑐1/𝑐2 = 2/5 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.