Chapter ISG, Problem 6.6.1P

To determine

To graph and describe the solution

Explanation of Solution

Given information:

  $\begin{array}{l}2x+y\ge 2\\ x-y>1\end{array}$

Graph:

The blue line represents $2x+y\ge 2$ and,

The green line represents $x-y>1$ .

  

Interpretation:

Given equation is $2x+y\ge 2$

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=0	(1,0)
-1	2(-1)+y=2	y=4	(-1,4)

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,

  $2\left(0\right)+0\ge 2$

This gives,

  $0\ge 2$

As the above statement is false, the shading of the graph will be away from origin.

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

  

Now, the given line is 1 $x-y>1$

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

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

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,

3 $x-y>1$

0-0>1

As the above statement is false, the shading of the graph will be away from origin.

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