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)

Question

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)

snowflake0531 · Answer

Are you allowed to use desmos or a graphing calculator for this?

carmelle · Answer

Its this a test?

snowflake0531 · Answer

https://www.desmos.com/calculator/i90rti9dyw That's the graph on desmos

snowflake0531 · Answer

Part A is easier for you to figure out yourself

snowflake0531 · Answer

Part B, looking at Desmos (8,2) is not a solution for both.

snowflake0531 · Answer

But it says 'Justify your answer mathematically'
So, you'd have to plug (8,2) in both equations
x + 3y ≤ 8
x + y ≥ 2
8+6 <8
Not true, already, it proves that this is wrong