# Solve the given inequality graphically in two-dimensional plane: x - y ≤ 2

**Solution:**

The graphical representation of x - y = 2 is given in the figure below.

This line divides the XY plane into 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,

0 - 0 ≤ 2 or 0 ≤ 2, which is true

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

Also, any point on the line satisfies the given inequality.

Thus, the solution region of the given inequality is the upper half-plane containing 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 5

## Solve the given inequality graphically in two-dimensional plane: x - y ≤ 2

**Summary:**

A linear inequation x - y ≤ 2 is given. We have found that the solution region of the given inequality is the upper half-plane containing the points including the line