Asap, will mark brainliest this is my last 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)

Here's what I get.

Step-by-step explanation:

(a) x + 3y ≤ 8

(b) x +   y ≥ 2

Part A

(i) Inequality (a)

Solve for y

The graph of y ≥ ⅓(8-x) is represented by the upper red line and all points in the shaded area below it. The line is solid because points on the line satisfy the condition.

ii) Inequality (b)

Solve for y

The graph of y ≥ 2 - x is represented by the lower blue line and all points in the shaded area above it. The line is solid because points on the line satisfy the condition.

The solution set lies in the purple area. It consists of all combinations of x and y that make y ≥ ⅓(8 - x) and y ≥ 2 - x.

A practical but not a mathematical condition is that all values of x and y must be zero or positive numbers (for example, you can't have -2 servings of food), so I have plotted only the numbers in the first quadrant.

Part B

Substitute (8,2)into each inequality

(i) Inequality (a)

FALSE.

ii) Inequality (b)

TRUE.

The point (8, 2) satisfies one inequality but not the other.

It is in the blue area but not the purple area of the graph, so it is not in the solution area for the system.

Part C

I will choose the point (2, 1).

x + 3y = 2 + 3×1 =2 + 3 = 5

x + y = 3

x represents a serving of dry food and y represents a serving of wet food.

The point (2, 1) means that she can buy three servings of food (> 2) —  two of dry and one of wet) —  for $5 (< $8).

Part A: Answer in explanation area. Picture 2 is the final solution.

Part B: No. It is not in the shaded region (orange) or either line in quadrant 1. I also provided an algebraic reason in the explanation.

Part C: Answer in explanation. (I chose (3,0) and provided a picture of the chosen point in picture 4).

Step-by-step explanation:

Part A:

I'm going to solve both inequalities for y.

Subtract on both sides:

Reorder right side:

Divide both sides by 3:

So this means I will shade below the line since we have y is less than.

I'm going to graph using the x- and y- intercepts.

To find the x-intercept set y=0 giving you which implies x=8[/tex].

To find the y-intercept set x=0 giving you which implies giving us .

So I graphed the two points (8,0) and (0,2.7) roughly on my coordinate plane.

Remember I'm going to shade below it.

I graphed those 2 points in blue. The line (in dark green) was solid because of the equal part of the inequality.

I symbolized the shading for this inequality in light green.

Subtract on both sides:

Reorder right hand side:

So the y-intercept is 2 and the slope is -1 (-1/1=down 1/right 1).

I'm going to graph (0,2) in red and the point (0+1,2-1)=(1,1) in red.

This line is also solid and I will connect them with a dark purple line.

The shading is above because it said y greater than.

The intersection of the the shaded regions along with the boundary lines in quadrant 1 are a solution to the inequality. So where you see purple and green is the area we are talking about.; the area, between the lines in quadrant 1.

Part B:

(8,2) is in picture 3.

(8,2) is not on either line in Quadrant 1 and it is also not located between them in the shaded region.

Therefore, it is not a solution.

We can also verify this algebraically.

In order for it to be a solution it must satisfy both inequalities.

with :

is not true so (8,2) is not a solution and we don't even have to check the second inequality as it had to be a solution to both.

Part C:

Let's choose (3,0).

x represents the number of dry food.

y represents the number of wet food.

So this means we just but 3 things of dry food and no wet food.

3 things of dry food will feed 2 dogs plus 1 more.

This will also cost us 3+3(0)=3 dollars which is less than 8 dollars.

is this part of a question or something