NCERT Solutions for Class 11 Maths Chapter 6- Linear Inequalities Exercise 6.2

The second exercise of this chapter is based on the topic Graphical Solution of Linear Inequalities in Two Variables.The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. Learn the graphical method of problem solving by practicing the questions given in Exercise 6.2 of NCERT Solutions for Class 11 Maths Chapter 6- Linear Inequalities.

The NCERT textbook provides plenty of questions for the students to solve and practice. Solving the NCERT Solutions for Class 11 Maths and practicing is more than enough to score high in the class 11 examinations. But the students should make sure that they practise every problem given in the textbook repeatedly till the concept gets clear.

Download PDF of NCERT Solutions for Class 11 Maths Chapter 6- Linear Inequalities Exercise 6.2

Solutions for Class 11 Maths Chapter 6 – Exercise 6.2

Solve the following inequalities graphically in two-dimensional plane:

1. x + y < 5

Solution:

Given x + y < 5

Consider

Now draw a dotted line x + y = 5 in the graph (∵ x + y = 5 is excluded in the given question)

Now Consider x + y < 5

Select a point (0, 0)

⇒ 0 + 0 < 5

⇒ 0 < 5 (this is true)

∴ Solution region of the given inequality is below the line x + y = 5. (That is origin is included in the region)

The graph is as follows:

2. 2x + y ≥ 6

Solution:

Given 2x + y ≥ 6

Now draw a solid line 2x + y = 6 in the graph (∵2x + y = 6 is included in the given question)

Now Consider 2x + y ≥6

Select a point (0, 0)

⇒ 2 × (0) + 0 ≥ 6

⇒ 0 ≥ 5 (this is false)

∴ Solution region of the given inequality is above the line 2x + y = 6. (Away from the origin)

The graph is as follows:

3. 3x + 4y ≤ 12

Solution:

Given 3x + 4y ≤ 12

Now draw a solid line 3x + 4y = 12 in the graph (∵3x + 4y = 12 is included in the given question)

Now Consider 3x + 4y ≤ 12

Select a point (0, 0)

⇒ 3 × (0) + 4 × (0) ≤ 12

⇒ 0 ≤ 12 (this is true)

∴ Solution region of the given inequality is below the line 3x + 4y = 12. (That is origin is included in the region)

The graph is as follows:

4. y + 8 ≥ 2x

Solution:

Given y + 8 ≥ 2x

Now draw a solid line y + 8 = 2x in the graph (∵y + 8 = 2x is included in the given question)

Now Consider y + 8 ≥ 2x

Select a point (0, 0)

⇒ (0) + 8 ≥ 2 × (0)

⇒ 0≤ 8 (this is true)

∴ Solution region of the given inequality is above the line y + 8 = 2x. (That is origin is included in the region)

The graph is as follows:

5. x – y ≤ 2

Solution:

Given x – y ≤ 2

Now draw a solid line x – y = 2 in the graph (∵ x – y = 2 is included in the given question)

Now Consider x – y ≤ 2

Select a point (0, 0)

⇒ (0) – (0) ≤ 2

⇒ 0 ≤ 12 (this is true)

∴ Solution region of the given inequality is above the line x – y = 2. (That is origin is included in the region)

The graph is as follows:

6. 2x – 3y > 6

Solution:

Given 2x – 3y > 6

Now draw a dotted line 2x – 3y = 6 in the graph (∵2x – 3y = 6 is excluded in the given question)

Now Consider 2x – 3y > 6

Select a point (0, 0)

⇒ 2 × (0) – 3 × (0) > 6

⇒ 0 > 5 (this is false)

∴ Solution region of the given inequality is below the line 2x – 3y > 6. (Away from the origin)

The graph is as follows:

7. – 3x + 2y ≥ – 6

Solution:

Given – 3x + 2y ≥ – 6

Now draw a solid line – 3x + 2y = – 6 in the graph (∵– 3x + 2y = – 6 is included in the given question)

Now Consider – 3x + 2y ≥ – 6

Select a point (0, 0)

⇒ – 3 × (0) + 2 × (0) ≥ – 6

⇒ 0 ≥ – 6 (this is true)

∴ Solution region of the given inequality is above the line – 3x + 2y ≥ – 6. (That is origin

is included in the region)

The graph is as follows:

8. y – 5x < 30

Solution:

Given y – 5x < 30

Now draw a dotted line 3y – 5x = 30 in the graph (∵3y – 5x = 30 is excluded in the given question)

Now Consider 3y – 5x < 30

Select a point (0, 0)

⇒ 3 × (0) – 5 × (0) < 30

⇒ 0 < 30 (this is true)

∴ Solution region of the given inequality is below the line 3y – 5x < 30. (That is origin is included in the region)

The graph is as follows:

9. y < – 2

Solution:

Given y < – 2

Now draw a dotted line y = – 2 in the graph (∵ y = – 2 is excluded in the given question)

Now Consider y < – 2

Select a point (0, 0)

⇒ 0 < – 2

⇒ 0 < 30 (this is false)

∴ Solution region of the given inequality is below the line y < – 2. (That is Away from the origin)

The graph is as follows:

10. x > – 3

Solution:

Given x > – 3

Now draw a dotted line x = – 3 in the graph (∵x = – 3 is excluded in the given question)

Now Consider x > – 3

Select a point (0, 0)

⇒ 0 > – 3

⇒ 0 > – 3 (this is true)

∴ Solution region of the given inequality is right to the line x > – 3. (That is origin is included in the region)

The graph is as follows:

Access other exercise solutions of Class 11 Maths Chapter 6- Linear Inequalities

Exercise 6.1 Solutions 26 Questions

Exercise 6.3 Solutions 15 Questions

Miscellaneous Exercise On Chapter 6 Solutions 14 Questions