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Ex 3.2, 4 - Which of the pairs of linear equations are - Ex 3.2

Ex 3.2, 4 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 2
Ex 3.2, 4 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 3 Ex 3.2, 4 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 4 Ex 3.2, 4 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables - Part 5

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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

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.