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Ex 6.3, 11 - Solve: 2x + y >= 4, x + y <= 3, 2x - 3y <= 6 - Graph - 2 or more Equation

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  1. Chapter 6 Class 11 Linear Inequalities
  2. Serial order wise
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Ex6.3, 11 Solve the following system of inequalities graphically: 2x + y ≥ 4, x + y ≤ 3, 2x – 3y ≤ 6 First we solve 2x + y ≥ 4 Lets first draw graph of 2x + y = 4 Drawing graph Checking for (0,0) Putting x = 0, y = 0 2x + y ≥ 6 2(0) + (0) ≥ 6 0 ≥ 6 which is false So, we shade right side of line Hence origin does not lie in plane 2x + y ≥ 6 First we solve x + y ≤ 3 Lets first draw graph of x + y = 3 Drawing graph Checking for (0,0) Putting x = 0, y = 0 x + y ≤ 3 0 + 0 ≤ 3 0 ≤ 3 which is true So, we shade left side of line Hence origin does not lie in plane x + y ≤ 3 Now we solve 2x – 3y ≤ 6 Lets first draw graph of 2x – 3y = 6 Drawing graph Checking for (0,0) Putting x = 0, y = 0 2x - 3y ≤ 6 2(0) – 3(0) ≤ 6 0 ≤ 6 which is true Hence origin lies in plane x + y ≤ 3 So, we shade left upper side of line Hence the shaded region represents the given inequality

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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