Linear Inequalities in Two Variables 

 

6.1  Linear Inequalities in Two Variables 
 
Inequalities are used to describe the relationship between two quantities that are not equal. 
 
  Example   
     
 

Anne wants to buy some revision books and exercise books at a book exhibition. 

She finds that the price of a reference book is \(\text{RM}15\) and the price of exercise book is \(\text{RM}10\).

The maximum amount of money that Anne can spend is \(\text{RM}100\).

Represent the above situation in an appropriate form of linear inequality. 

 
     
 

Solution

Let's \(x= \text{reference book}\)\(y= \text{exercise book}\).

Thus, 

\(15x + 10 y\leq100\) or \(10y \leq100-15x\)

 
 
Inequality can also be represented on a Cartesian plane by shading the region that satiesfies inequality. 
 
  Example  
     
   
     
 
Relationship between a point on a Cartesian plane with the inequality \(y >mx +c, y < mx+c, y \geq mx+c, \text{or}, y\leq mx+c\)
 
     
\(>,<\)  
  • Points that lie in the region above or below a straight line \(y=mx+c\)
   
 
  • The straight line is drawn using a dashed line
     
\(\geq, \leq\)  
  • Points that lie on the straight line\(y=mx +c\) including the region above or below
   
 
  • The straight line is drawn using a solid line
 

 

Linear Inequalities in Two Variables 

 

6.1  Linear Inequalities in Two Variables 
 
Inequalities are used to describe the relationship between two quantities that are not equal. 
 
  Example   
     
 

Anne wants to buy some revision books and exercise books at a book exhibition. 

She finds that the price of a reference book is \(\text{RM}15\) and the price of exercise book is \(\text{RM}10\).

The maximum amount of money that Anne can spend is \(\text{RM}100\).

Represent the above situation in an appropriate form of linear inequality. 

 
     
 

Solution

Let's \(x= \text{reference book}\)\(y= \text{exercise book}\).

Thus, 

\(15x + 10 y\leq100\) or \(10y \leq100-15x\)

 
 
Inequality can also be represented on a Cartesian plane by shading the region that satiesfies inequality. 
 
  Example  
     
   
     
 
Relationship between a point on a Cartesian plane with the inequality \(y >mx +c, y < mx+c, y \geq mx+c, \text{or}, y\leq mx+c\)
 
     
\(>,<\)  
  • Points that lie in the region above or below a straight line \(y=mx+c\)
   
 
  • The straight line is drawn using a dashed line
     
\(\geq, \leq\)  
  • Points that lie on the straight line\(y=mx +c\) including the region above or below
   
 
  • The straight line is drawn using a solid line