Class 11: Linear Inequations – Exercise 15.6

Question 1: Solve the following systems of linear inequations graphically:

i)

ii)

iii)

iv)

v)

Answer:

i)

ii)

iii)

iv)

v)

Question 2: Show that the solution set of the following linear inequations is empty set:

i)

ii)

Answer:

i) There is no common areas between the inequations. Hence there is no solution or the solution is null set.

ii) There is no common areas between the inequations. Hence there is no solution or the solution is null set.

Question 3: Find the linear inequations for which the shaded area in the figure below is the solution set. Draw the diagram of the solution set of the linear in-equations.Answer:

The inequations are

Question 4: Find the linear inequations for which the solution set is the shaded region given in the figure below. Answer:

The inequations are

Question 5: Show that the solutions set of the following linear inequations is an unbound set:

Answer:

Solutions set of the following linear inequations is an unbound set.

Question 6: Solve the following systems of inequations graphically:

i)

ii)

iii)

iv)

Answer:

i)

ii)

iii)

iv)

Question 7: Show that the following system of linear inequations have some solution: 

Answer:There is no solution set for the given inequalities.

Question 8:  Show that the solution set of the following system of linear inequations is an unbounded region 

Answer:

We see that the solution set is the unbounded region.