Ex 3.1, 4 (i) - Chapter 3 Class 10 Pair of Linear Equations in Two Variables

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Ex 3.1, 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