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

Doorsteptutor material for CBSE is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

**Question 15:**

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

**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

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:

**Answer:**

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

**Answer:**

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