NCERT Class 11-Math's: Chapter –6 Linear Inequalities Part 7

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Question 15:

Find the linear inequalities for which the shaded region in the given figure is the solution set.

Chapter 6-Question15-Linear Inequalities Fig 6.5

Linear Inequalities Fig 6.5

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Answer:

Question 16:

Show that the following system of linear inequalities has no solution

Answer:

Let’s plot the region of each inequality and then find the common region of all

Common region

x

3

1

y

0

1

Also, satisfies the , hence region is towards the origin

Line:

Common region

x

0

4

y

3

0

Also, satisfies the , hence region is towards the origin

implies that region is right to the y-axis and implies that region is up above the line ,

Question 17:

Solve the following system of linear inequalities:

Answer:

Let’s plot the region of each inequality and then find the common region of all

Common region

x

0

8

y

12

0

Also, doesn’t satisfy the , hence region is away from the origin

Line:

Common region

x

0

5

y

15

0

Also, satisfies the , hence region is towards the origin

implies that region is right to the line ,

Question 18:

Show that the solution set of the following system of linear inequalities is an unbounded region

Answer:

Let’s plot the region of each inequality and then find the common region of all

Line:

common region

x

0

8

y

4

0

Also, doesn’t satisfy the , hence region is away from the origin

Line:

common region

x

0

10

y

5

0

Also, doesn’t satisfy the , hence region is away from the origin