Chapter 13.4, Problem 5PSB

(a)

To determine

To find: The graph for the solution of the given system of inequalities.

Answer to Problem 5PSB

The required graph is shown in Figure 1.

Explanation of Solution

Given:

The given inequality is,

  $\begin{array}{l}y\ge x+4\\ y\le -2x+6\end{array}$

Calculation:

Consider the given inequality is,

  $\begin{array}{l}y\ge x+4\\ y\le -2x+6\end{array}$

The graph for the given inequality is shown in Figure 1

  

Figure 1

(b)

To determine

To find: The graph for the solution of the given system of inequalities.

Answer to Problem 5PSB

The required graph is shown in Figure 2.

Explanation of Solution

Given:

The given inequality is,

  $\begin{array}{l}x+y\le 4\\ 2x-y\le 6\\ x\ge 0\end{array}$

Calculation:

Consider the given inequality is,

  $\begin{array}{l}x+y\le 4\\ 2x-y\le 6\\ x\ge 0\end{array}$

The graph for the given inequality is shown in Figure 2

  

Figure 2

(c)

To determine

To find: The graph for the solution of the given system of inequalities.

Answer to Problem 5PSB

The required graph is shown in Figure 3.

Explanation of Solution

Given:

The given inequality is,

  $\begin{array}{l}x+y>12\\ x-y\le 4\end{array}$

Calculation:

Consider the given inequality is,

  $\begin{array}{l}x+y>12\\ x-y\le 4\end{array}$

The graph for the given inequality is shown in Figure 3

  

Figure 3

(d)

To determine

To find: The graph for the solution of the given system of inequalities.

Answer to Problem 5PSB

The required graph is shown in Figure 4.

Explanation of Solution

Given:

The given inequality is,

  $\begin{array}{l}4y-3x<6\\ y<3x\\ 2x<6-3y\end{array}$

Calculation:

Consider the given inequality is,

  $\begin{array}{l}4y-3x<6\\ y<3x\\ 2x<6-3y\end{array}$

The graph for the given inequality is shown in Figure 4

  

Figure 4

(e)

To determine

To find: The graph for the solution of the given system of inequalities.

Answer to Problem 5PSB

The required graph is shown in Figure 5.

Explanation of Solution

Given:

The given inequality is,

  $\begin{array}{l}y>\left|x-1\right|\\ x+3y<12\end{array}$

Calculation:

Consider the given inequality is,

  $\begin{array}{l}y>\left|x-1\right|\\ x+3y<12\end{array}$

The graph for the given inequality is shown in Figure 5

  

Figure 5

(f)

To determine

To find: The graph for the solution of the given system of inequalities.

Answer to Problem 5PSB

The required graph is shown in Figure 6.

Explanation of Solution

Given:

The given inequality is,

  $\begin{array}{l}y<2x+5\\ 2x-y<3\end{array}$

Calculation:

Consider the given inequality is,

  $\begin{array}{l}y<2x+5\\ 2x-y<3\end{array}$

The graph for the given inequality is shown in Figure 6

  

Figure 6