Chapter 6.6, Problem 2P

a.

To determine

To write: a system of inequalities that represented by the given graph.

Answer to Problem 2P

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

Explanation of Solution

Given information: a figure is given as follows-

  

Since the dark line passes through the points (0, 1) and (-2, 0). So, its equation is $\begin{array}{l}\frac{y-1}{x-0}=\frac{0-1}{-2-0}=\frac{1}{2}\\ \Rightarrow \frac{y-1}{x-0}=\frac{1}{2}\\ \Rightarrow 2y-2=x\\ \Rightarrow x-2y=-2\end{array}$

This divides the xy-plane into two regions and two inequalities are possible such as $x-2y\ge -2$ and $x-2y\le -2$ .

Take any point from the colored region and put this value in the above inequalities which satisfies is the required inequality.

Such as take a point (0, 0) from the colored region, the inequality which contains this point is $x-2y\ge -2$ . Hence this is the required inequality.

Similarly the other required inequality is $2y+x<2$ .

b.

To determine

To find: whether the point where the boundary lines intersect is a solution of the system.

Answer to Problem 2P

Yes

Explanation of Solution

Given information: a figure is given as follows-

  

Since the point of intersection of boundary lines lies on the dark lines which is a part of solution.

Hence point of intersection of boundary lines is a solution of the system.