Solve the following system of inequalities graphically: 2x - y > 1, x - 2 y < - 1

Solution:

2x - y > 1 ....(1)

x - 2 y < - 1....(2)

The graphs of the lines, 2x - y = 1 and x - 2 y = - 1 are drawn in the figure below.

Inequality 2x - y > 1 represents the region below the line, 2x - y = 1 (excluding the line 2x - y = 1)

Inequality x - 2 y < - 1 represents the region on the right hand side of the line, x - 2 y = - 1 (excluding the line x - 2 y = - 1)

Hence, the solution of the given system of linear inequalities is represented by the common shaded region excluding the points on the respective lines as follows:

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.3 Question 5

Solve the following system of inequalities graphically: 2x - y > 1, x - 2 y < - 1

Summary:

Linear inequations 2x - y > 1, x - 2 y < - 1 is given. We have found that the solution of the given system of linear inequalities is represented by the common shaded region excluding the points on the respective lines