Chapter 7.5, Problem 76E

a.

To determine

Match the system of inequalities with the graph of its solution.

Answer to Problem 76E

  

Explanation of Solution

Given information:

Match the system of inequalities with the graph of its solution.

  

[The graphs are labelled (i), (ii), (iii), and (iv)]

  $\{\begin{array}{l}{x}^2+y^2\le 16\\ x+y\ge 4\end{array}$

Calculation:

Consider the following inequalities

  $\begin{array}{l}{x}^2+y^2\le 16\\ x+y\ge 4\end{array}$

First use maple to draw the graph of above inequalities.

  

From the above graph, it shows that the shaded region is inside the circle $x^2+y^2=16$ and above the line $x+y=4$ .

Hence, the option matches to $\boxed{(\text{iv})}$ .

b.

To determine

Match the system of inequalities with the graph of its solution.

Answer to Problem 76E

  

Explanation of Solution

Given information:

Match the system of inequalities with the graph of its solution.

  

  $\begin{array}{l}{x}^2+y^2\le 16\\ x+y\le 4\end{array}$

Calculation: Consider the following inequalities

  $\begin{array}{l}{x}^2+y^2\le 16\\ x+y\le 4\end{array}$

First use maple to draw the graph of above inequalities.

  

From the above graph, it shows that the shaded region is inside the circle $x^2+y^2=16$ and below the line $x+y=4$ .

Hence, the option matches to $\boxed{(\text{ii})}$ .

c.

To determine

Match the system of inequalities with the graph of its solution

Answer to Problem 76E

  

Explanation of Solution

Given information:

Match the system of inequalities with the graph of its solution.

  

  $\begin{array}{l}{x}^2+y^2\ge 16\\ x+y\ge 4\end{array}$

Calculation: Consider the following inequalities

  $\begin{array}{l}{x}^2+y^2\ge 16\\ x+y\ge 4\end{array}$

First use maple to draw the graph of above inequalities.

  

From the above graph, it shows that the shaded region is outside the circle $x^2+y^2=16$ and above the line $x+y=4$ .

Hence, the option matches to $\boxed{(\text{iii})}$ .

d.

To determine

Match the system of inequalities with the graph of its solution.

Answer to Problem 76E

  

Explanation of Solution

Given information:

Match the system of inequalities with the graph of its solution.

  

  $\begin{array}{l}{x}^2+y^2\ge 16\\ x+y\le 4\end{array}$

Calculation: Consider the following inequalities

  $\begin{array}{l}{x}^2+y^2\ge 16\\ x+y\le 4\end{array}$

First use maple to draw the graph of above inequalities.

  

From the above graph, it shows that the shaded region is outside the circle $x^2+y^2=16$ and below the line $x+y=4$ .

Hence, the option matches to $\boxed{(\text{i})}$ .