Chapter 6.6, Problem 35PPE

To determine

Towrite:The system of linear inequalities for given graph with given characteristics.

Answer to Problem 35PPE

The system of inequalities with required characteristics is $x>2$ , $y>4$ , $x<-3$ , $y<-3$ .

Explanation of Solution

Given information:

The graph of system of inequalities is shown in Figure-1 here.

The characteristic of inequalities that there is no solution in Quadrants I, II, III and IV.

Method used:

Find equations of lines (boundaries of shaded portions) and write inequalities corresponding to obtained lines.

Calculations:

The given Quadrants I, II, III, and IV are bounded by the lines

  $x=2$........(1)

  $y=4$........(2)

  $x=-3$........(3)

  $y=-3$........(4)

Therefore, the system of inequalities whose solutions do not lie in Quadrants I, II, III, and IV is the region beyond these lines given by

  $x>2$........(5)

  $y>4$........(6)

  $x<-3$........(7)

  $y<-3$........(8)

Verification:

The graph for the system of inequalities $x>2$ , $y>4$ , $x<-3$ , and $y<-3$ is shown in Figure-3.

  

Hence, the system of inequalities with required characteristics is $x>2$ , $y>4$ , $x<-3$ , $y<-3$ .

Conclusion:

The system of inequalities with required characteristics is $x>2$ , $y>4$ , $x<-3$ , $y<-3$ .