Solve the following system of inequalities graphically: 2x + y ≥ 6, 3x + 4 y ≤ 12

Solution:

2x + y ≥ 6 ....(1)

3x + 4 y ≤ 12 ....(2)

The graphs of the lines, 2x + y = 6 and 3x + 4 y = 12 are drawn in the figure below

Inequality 2x + y ≥ 6 represents the region below the line, 2x + y = 6 (including the line 2x + y = 6).

Inequality 3x + 4 y ≤ 12 represents the region on the right hand side of the line, 3x + 4 y = 12 (including the line 3x + 4 y = 12)

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 3

Solve the following system of inequalities graphically: 2x + y ≥ 6, 3x + 4 y ≤ 12

Summary:

Linear inequations 2x + y ≥ 6, 3x + 4 y ≤ 12 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