Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Solution of Linear Inequalities in two variable

\to Solution:

Values of   x & y , 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  ax+by=c, \qquad a \neq 0, b \neq 0

There are 3 possibilities namely:

(i)  ax+by = c

(ii) ax+by > c

(iii) ax+by < c

Often we use mostly  ax+by \leq c or  ax+by \geq c

The above region said that all the points in this region satisfy the inequality  ax+by \leq c
All the points in the above region satisfy the inequality  ax +by \geq c

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 (0,0) .

(iii) If an inequality is of the type  ax+by \geq c or  ax+by \leq c , then the points on the line  ax+by=c are  also included in the solution region.

(iv) If an inequality is of the form  ax+by > c or  ax+by < c , then the points on the line  ax+by =c are not to be included in the solution region.

 

 

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