Ex 6.3, 15 - Solve graphically: x + 2y <= 10, x + y >= 1 - Graph - 2 or more Equation

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  1. Chapter 6 Class 11 Linear Inequalities
  2. Serial order wise
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Ex 6.3, 15 Solve the following system of inequalities graphically: x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0 First we solve x + 2y ≤ 10 Lets first draw graph of x + 2y = 10 Drawing graph Checking for (0,0) Putting x = 0,y = 0 x + 2y ≤ 10 0+2(0)≤10 0 ≤ 10 which is true So, we shade left side of line Hence origin lies in plane x + 2y ≥ 10 Now we solve x + y ≥ 1 Lets first draw graph of x + y = 1 Drawing graph Checking for (0,0) Putting x = 0, y = 0 x + y ≥ 1 0 + 0 ≥ 1 0 ≥ 1 which is false Hence origin does not lie in plane x + y ≥ 1 So, we shade right upper side of line Now we solve x – y ≤ 0 Lets first draw graph of x – y = 0 Drawing graph Checking for (10,0) Putting x = 10, y = 0 x – y ≤ 0 10 – 0 ≤ 0 10 ≤ 0 which is false. Hence (10,0) does not lie in plane x > y So, we shade left side of line Also, given x ≥ 0, y ≥ 0 So, shaded region will lie in first quadrant Hence the shaded region represents the given inequality

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