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.

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

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

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x + 3y ≤ 8

x + y ≥ 2

write both of them like linear relationships in the slope-intercept

y ≤ -(1/3)*x + 8/3

y  ≥ 2 - x

a.

the graph of y ≤ -(1/3)*x + 8/3 is a solid line

y = -(1/3)*x + 8/3

(not sure how to add a graph but use desmos to help you graph)

b.

see if (8, 2) is a solution

so replace x by 8 and y by 2 in both inequalities

first inequality:

8 + 3*2 ≤ 8

8 + 6  ≤ 8

14  ≤ 8

False, 14 is not smaller than or equal to 8, then we already can see that (8, 2) is not a solution.

c.

We can see that one possible solution is (2, 1)

first inequality:

2  + 3*1 ≤ 8

5 ≤ 8

True.

Second inequality:

1 + 2 ≥ 2

3 ≥ 2

True.

(2, 1) is the solution

x = 2

y = 1

She can buy 2 dry food servings and 1 wet food serving.

hope this helped :)

why can't you?

step-by-step explanation:

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