Chapter ISG, Problem 6.6.3P

To determine

To graph and describe the system of linear inequalities

Explanation of Solution

Given information:

  $\begin{array}{l}x+y\ge 0\\ 2x+y>-2\\ x+3y>-3\end{array}$

Graph:

  

Interpretation:

Given inequality is $x+y\ge 0$

To plot the inequality on graph, the x& y points are to be identified.

x	Inequality Calculation	y	Point
0	0+ y=0	y=2	(0,0)
1	1+ y=0	y=-1	(1,-1)
-1	-1+ y=0	y=4	(-1,1)

Since it is an inequality, the shading of the graph is to be determined. To determine shading,

The truth or falsity of the equation is to verified at Origin (0,0).

On putting x & y as 0,

  $0+0\ge 0$

This gives $0\ge 0$

As the above statement is true, the shading of the graph will be towards origin.

On plotting the points on graph, the solution will look as below-

  

Now given line is $2x+y>-2$

To plot the inequality on graph, the x& y points are to be identified.

x	Inequality Calculation	y	Point
0	2(0)+y=-2	y=-2	(0,-2)
1	2(1)+y=-2	y =-4	(1,-4)
-1	2(-1)+y=-2	y =0	(-1,0)

Since it is an inequality, the shading of the graph is to be determined. To determine shading,

The truth or falsity of the equation is to verified at Origin (0,0).

On putting x & y as 0,

  $2(0)+(0)>-2$

As the above statement is true, the shading of the graph will be towards origin.

On plotting the points on graph, the solution will look as below-

  

Now, the given line is $x+3y>-3$

To plot the inequality on graph, the x& y points are to be identified.

x	Inequality Calculation	y	Point
0	0+3y=-3	y=-1	(0,-1)
-3	-3+3y=-3	y =0	(-3,0)
-6	-6+3y=-3	y =1	(-3,1)

Since it is an inequality, the shading of the graph is to be determined. To determine shading,

the truth or falsity of the equation is to verified at Origin (0,0).

On putting x & y as 0,

  $0+3(0)>-3$

This gives, $0+0>-3$

As the above statement is true, the shading of the graph will be towards origin.

On plotting the points on graph, the solution will look as below-