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Example  15 - Chapter 6 - Solve x + 2y <= 8 , 2x + y <= 8

Example  15 - Chapter 6 Class 11 Linear Inequalities - Part 2
Example  15 - Chapter 6 Class 11 Linear Inequalities - Part 3
Example  15 - Chapter 6 Class 11 Linear Inequalities - Part 4
Example  15 - Chapter 6 Class 11 Linear Inequalities - Part 5

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Transcript

Example 15 Solve the following system of inequalities graphically x + 2y ≤ 8 , 2x + y ≤ 8 , x ≥ 0 , y ≥ 0 First we solve x + 2y ≤ 8 Lets first draw graph of x + 2y = 8 Putting x = 0 in (1) 0 + 2y = 8 2y = 8 y = 8/2 y = 4 Putting y = 0 in (1) x + 2(0) = 8 x + 0 = 8 x = 8 Points to be plotted are (0,4) , (8,0) Drawing graph Checking for (0,0) Putting x = 0, y = 0 x + 2y ≤ 8 (0) + 2(0) ≤ 8 0 ≤ 8 which is true Hence origin lies in plane x + 2y ≤ 8 So, we shade left side of line Now, we solve 2x + y ≤ 8 Lets first draw graph of 2x + y = 8 Putting x = 0 in (2) 2(0) + y = 6 0 + y = 6 y = 8 Putting y = 0 in (2) 2x + (0) = 8 2x = 8 x = 8/2 x = 4 Points to be plotted are (0,8) , (4,0) Drawing graph Checking for (0,0) Putting x = 0,y = 0 2x + y ≤ 8 0 + 0 ≤ 8 0 ≤ 8 which is false Hence origin does not lie in plane 2x + y ≤ 8 So, we shade left side of line Also given that x ≥ 0 , y ≥ 0 Hence the shaded region will lie in the first quadrant. Hence the shaded region represents the given inequality

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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.