# 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.

Question 16:

Show that the following system of linear inequalities has no solution

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

 x 3 1 y 0 1

Also, satisfies the , hence region is towards the origin

Line:

 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:

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

 x 0 8 y 12 0

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

Line:

 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

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

Line:

 x 0 8 y 4 0

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

Line:

 x 0 10 y 5 0

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