Solve the following system of inequalities graphically: 2x + y ≥ 4, x + y ≤ 3, 2x - 3y ≤ 6

Solution:

2x + y ≥ 4 ....(1)

x + y ≤ 3 ....(2)

2x - 3y ≤ 6 ....(3)

The graph of the lines, 2x + y = 4, x + y = 3 and 2x - 3y = 6 , are drawn in the figure below.

Inequality 2x + y ≥ 4 represents the region above the line, 2x + y = 4 (including the line).

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

Inequality 2x - 3y ≤ 6 represents the region above the line, 2x - 3y = 6 (including the line).

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 11

Solve the following system of inequalities graphically: 2x + y ≥ 4, x + y ≤ 3, 2x - 3y ≤ 6.

Summary:

Linear inequations 2x + y ≥ 4, x + y ≤ 3, 2x - 3y ≤ 6 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