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Linear Inequalities in Two Variables:
The inequalities of the form  ,  ,  , where  ,  , c are constants, are called the linear inequalities in two variable.
The points  which satisfy the linear inequality in two variable 'x' and 'y' from its solution.
Graphing the Solution Region of Linear Inequality in Two Variables:
Example:
Graph the solution set of the linear inequality  in xy–plane.
Solution:
We have
 —————— (A)
The corresponding equation of inequality A
 —————— (1)
For x–intercept:
Put  in eq (1)
 
 
 
For y–intercept:
Put  in eq (1)
 
 
 
Test:
Put origin  in eq (A)
 which is true.
 Solution set of inequality lies origin side.
Example:
Graph the solution set of the linear inequality  in xy–plane.
Solution:
We have
 —————— (A)
The corresponding equation of inequality A
 —————— (1)
For x–intercept:
Put  in eq (1)
 
   
 x–intercept 
For y–intercept:
Put  in eq (1)
 
 
 
 y–intercept 
Test:
Put origin  in eq (A)
  which is false.
 Solution set lies other side of origin.
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