Ex 6.3, 13 - Solve 4x + 3y <= 60, y >= 2x, x >= 3 - Ex 6.3

Ex 6.3,  13 - Chapter 6 Class 11 Linear Inequalities - Part 2
Ex 6.3,  13 - Chapter 6 Class 11 Linear Inequalities - Part 3
Ex 6.3,  13 - Chapter 6 Class 11 Linear Inequalities - Part 4
Ex 6.3,  13 - Chapter 6 Class 11 Linear Inequalities - Part 5

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Ex6.3, 13 Solve the following system of inequalities graphically: 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0 Now we solve 4x + 3y ≤ 60 Lets first draw graph of 4x + 3y = 60 Drawing graph Checking for (0,0) Putting x = 0, y = 0 4x + 3y ≤ 60 4(0) + 3(0) ≤ 60 0 ≤ 60 which is true Hence origin lies in plane 3x + 4y ≤ 60 So, we shade left side of line Now we solve y ≥ 2x Lets first draw graph of y = 2x Drawing graph Checking for (0,15) Putting x = 0, y = 15 y ≥ 2x 15 ≥ 2(0) 15 ≥ 0 which is true Hence (0, 15) lies in plane y ≥ 2x So, we shade left side of line Also, x ≥ 3 So, for all values of y, x = 3 Given x ≥ 3, so we shade right side of line Also, given x , y ≥ 0 So, the shaded region will line in 1st quadrant Hence the shaded region represents the given inequality

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo