Solve the given inequality graphically in two-dimensional plane: 2x + y ≥ 6

Solution:

The graphical representation of 2x + y = 6 is given in the figure below

This line divides the xy-plane in two half planes, I and II

Select a point (not on the line), which lies in one of the half planes, to determine whether the point satisfies the given inequality or not

We select the point as (0, 0).

It is observed that,

2 (0) + 0 ≥ 6 or 0 ≥ 6, which is false.

Therefore, half plane I is not the solution region of the given inequality

Also, it is evident that any point on the line satisfies the given inequality

Thus, the solution region of the given inequality is the shaded half plane II including the points on the line

This can be represented as follows:

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.2 Question 2

Solve the given inequality graphically in two-dimensional plane: 2x + y ≥ 6

Summary:

A linear inequation 2x + y ≥ 6 is given. We have found that the solution region of the given inequality is the shaded half plane II including the points on the line