Solve the following system of inequalities graphically:
4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0

Solution:

4x + 3y ≤ 60 ....(1)

y ≥ 2x ....(2)

x ≥ 3 ....(3)

The graph of the lines, 4x + 3y = 60 , y = 2x , and x = 3 , are drawn in the figure below.

Inequality 4x + 3y ≤ 60 represents the region below the line, 4x + 3y = 60 (including the line 4x + 3y = 60)

Inequality y ≥ 2x represents the region above the line, y = 2x (including the line y = 2x).

Inequality x ≥ 3 represents the region on the right-hand side of the line, x = 3 (including the line x = 3).

Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the respective lines as follows:

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.3 Question 13

Solve the following system of inequalities graphically: 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0

Summary:

Linear inequations 4x + 3y ≤ 60, y ≥ 2x, x ≥ 3, x, y ≥ 0 is given. We have found that the solution of the given system of linear inequalities is represented by the common shaded region including the points on the respective lines