### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Solution of Linear Inequalities in two variable

Lesson Progress
0% Complete Solution:

Values of & , which make inequalities true statements.

Graphical Representation:

In two variables the graph of the solution is drawn on a Cartesian Plane. A line divides the Cartesian Plane into two parts. Each part is known as half plane.

A vertical line will divide the plane into a left and right half-plane and a non-vertical line will divide the plane into lower and upper half-planes.

Let us consider the line There are possibilities namely:

(i) (ii) (iii) Often we use mostly or  The above region said that all the points in this region satisfy the inequality All the points in the above region satisfy the inequality

Notes:

(i) the region containing all the solutions of an inequality is called the Solution Region.

(ii) To check the points shaded region of inequality, we have to satisfy the inequation with the origin .

(iii) If an inequality is of the type or , then the points on the line are  also included in the solution region.

(iv) If an inequality is of the form or , then the points on the line are not to be included in the solution region.

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