Michelle has $8 and wants to buy a combination of dog food to feed at least two dogs at the animal shelter. a serving of dry food costs $1, and a serving of wet food costs $3.

this system of inequalities models the scenario:

x + 3y ≤ 8
x + y ≥ 2

part a: describe the graph of the system of inequalities, including shading and the types of lines graphed. provide a description of the solution set. (4 points)

part b: is the point (8, 2) included in the solution area for the system? justify your answer mathematically. (3 points)

part c: choose a point in the solution set and interpret what it means in terms of the real-world context. (3 points)

Part A) The graph in the attached figure (see the explanation)

Part B) The point (8,2) is not included in the solution area for the system

Part C) see the explanation

Step-by-step explanation:

Part A: Describe the graph of the system of inequalities

Let

x > the number of serving of dry food

y > the number of serving of wet food

we have

> inequality A

The solution of the inequality A is the shaded area below the solid line A

The equation of the solid line A is

The slope of the solid line A is negative

The y-intercept of the solid line A is (0,8/3)

The x-intercept of the solid line A is (8,0)

> inequality B

The solution of the inequality B is the shaded area above the solid line B

The equation of the solid line B is

The slope of the solid line B is negative

The y-intercept of the solid line B is (0,2)

The x-intercept of the solid line B is (2,0)

Therefore

The solution of the system is the shaded area  below the solid line A and above the solid line B

Remember that that the values of x and y cannot be a negative number

using a graphing tool

The graph in the attached figure

Part B: Is the point (8, 2) included in the solution area for the system? Justify your answer mathematically

we know that

If a point is a solution of the system, then the point must satisfy both inequalities of the system (makes true both inequalities)

For x=8, y=2

Verify inequality A

> is not true

so

the point not satisfy inequality A

therefore

The point is not included in the solution area for the system

Part C: Choose a point in the solution set and interpret what it means in terms of the real-world context

I choose the point (3,1) (is included in the solution area for the system)

That means

Michelle buy 3 serving of dry food and 1 serving of wet food

the slope of the first function is -3. (3/1)

the slope of the second function is 1. (13-10/6-3).

since |-3| is greater than |1|, the function with the steepest slope is the first.