Hurryy i am begging for ive been stuck for an hour
sarah has $8 and wants to buy a combination of cupcakes and fudge to feed at least four siblings. each cupcake costs $2, and each piece of fudge costs $1. this system of inequalities models the scenario:

2x + y ≤ 8
x + y ≥ 4

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, 10) 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:

Look at the image attached to my answer for the graph of the inequalities.

There are two different lines provided, one with a more negative slope than the other. The shaded area between them represents the solution set.

The green line is 2x+y≤8, the blue line is x+y≥4

Part B:

To test if (8, 10) is included, substitute x = 8 and y = 10 into both inequalities. If it doesn't satisfy one of them, then it isn't included in the solution area.

2(8) + 10 ≤ 8

16 + 10 ≤ 8

26 ≤ 8... 26 is NOT less then or equal to 8

Thus, (8, 10) cannot be a solution since the inequality is not true.

Part C:

I'm going to choose a random point from the graph, (2, 3). For your answer, any point in the shaded region where both x and y is positive will work.

The point (2, 3) means that Sarah can buy 2 cupcakes and 3 pieces of fudge to get at least 4 pastries for her siblings while staying within her 8 dollar budget.

Let me know if you need any clarifications. Happy Studying~

2x^2+5x+17

your welcome. : )