Solve the following system of inequalities graphically: x + y ≥ 4, 2x - y < 0

Solution:

x + y ≥ 4 ....(1)

2x - y < 0 ....(2)

The graphs of the lines, x + y = 4 and 2x - y = 0 are drawn in the figure below.

Inequality x + y ≥ 4 represents the region above the line, x + y = 4 (including the line x + y = 4)

It is observed that (1, 0) satisfies the inequality, 2x - y < 0 . Since, 2 (1) - 0 = 2 < 0

Therefore, Inequality 2x - y < 0 represents the half plane corresponding to the line, 2x - y = 0, containing the point (1, 0) (excluding the line 2x - y < 0).

Hence, the solution of the given system of linear inequalities is represented by the x + y = 4 and excluding the points common shaded region including the points on the line on line 2x - y = 0 as follows

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.3 Question 4

Solve the following system of inequalities graphically: x + y ≥ 4, 2x - y < 0

Summary:

Linear inequations x + y ≥ 4, 2x - y < 0 is given. We have found that the solution of the given system of linear inequalities is represented by the x + y = 4 and excluding the points common shaded region including the points on the line on line 2x - y = 0