Solve the following system of inequalities graphically: 3x + 2 y ≤ 12, x ≥ 1, y ≥ 2

Solution:

3x + 2 y ≤ 12 ....(1)

x ≥ 1 ....(2)

y ≥ 2 ....(3)

The graphs of the lines, 3x + 2 y = 12, x = 1, and y = 2, are drawn in the figure below

Inequality 3x + 2 y ≤ 12 represents the region below the line 3x + 2 y = 12 (including the line 3x + 2 y = 12).

Inequality x ≥ 1 represents the region on the right hand side of the line, x = 1 (including the line x = 1).

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

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 2

Solve the following system of inequalities graphically: 3x + 2 y ≤ 12, x ≥ 1, y ≥ 2

Summary:

Linear inequations 3x + 2 y ≤ 12, x ≥ 1, y ≥ 2 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