Solve the given inequality graphically in two-dimensional plane: 2x - 3y > 6

Solution:

The graphical representation of 2x - 3y = 6 is given as dotted line in the figure below.

This line divides the xy-plane in two half planes.

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) - 3(0) > 6 or 0 > 6 , which is false.

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

Also, any point on the line does not satisfy the given inequality

Thus, the solution region of the given inequality is the lower half plane that does not contain the points including the line

The solution region is represented by the shaded region as follows:

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.2 Question 6

Solve the given inequality graphically in two-dimensional plane: 2x - 3y > 6

Summary:

A linear inequation 2x - 3y > 6 is given. We have found that the solution region of the given inequality is the lower half plane that does not contain the points including the line