# NCERT Solutions for Class 11-science Maths Chapter 6 - Linear Inequalities

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## Chapter 6 - Linear Inequalities Exercise Ex. 6.3

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x + y ≥ 4   … (1)

2x – y < 0  … (2)

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

Inequality (1) 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.

[2(-1) – 0 = -2< 0]

Therefore, inequality (2) 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 common shaded region including the points on the line x + y = 4 and excluding the points on line 2x – y = 0 as follows:

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