Ex 6.3, 14 - Solve graphically: 3x + 2y <= 150, x + 4y <= 80 - 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, 14 Solve the following system of inequalities graphically: 3x + 2y ≤ 150, x + 4y ≤ 80, x ≤ 15, y ≥ 0, x ≥ 0 Now we solve 3x + 2y ≤ 150 Lets first draw graph of 3x + 2y = 150 Drawing graph Checking for (0,0) Putting x = 0, y = 0 3x + 2y ≤ 150 4(0)+ 3(0)≤ 150 0 ≤ 150 which is true Hence origin lies in plane 3x + 2y ≤ 150 So, we shade left side of line Now we solve x + 4y ≤ 80 Lets first draw graph of x + 4y = 80 Drawing graph Checking for (15,0) Putting x = 15, y = 0 y ≥ 2x 0 ≥ 2(15) 0 ≥ 30 which is false Hence (15,0) does not lie in plane y ≥ 2x So, we shade left side of line Also, x ≤ 15 So, for all values of y, x = 15 Given x ≤ 15, so we shade left side of line Also, given x, y ≥ 0 So, the shaded region will lie in 1st quadrant. Hence the shaded region represents the given inequality.

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