Hi! Can one of y'all just check my answers for me? I am just a bit unsure before I submit them. 100 Points. Thanks!

1. The set of linear equations provided describes the relationship between the number of minutes Max practices the guitar and piano every day. The equations are x+y=150 and y=x+80.

To solve the equations, we can start by substituting y in the first equation with the value of y from the second equation. This gives us x+(x+80)=150, which simplifies to 2x+80=150. We can then solve for x by subtracting 80 from both sides, giving us 2x=70, and dividing by 2, giving us x=35.

Substituting x=35 into the first equation, we can solve for y by subtracting x from both sides, giving us y=150-x, which simplifies y=115. Therefore, Max spends 115 minutes practicing the piano and 35 minutes practicing the guitar each day.

It is important to note that Max has a total practice time of 150 minutes, and therefore, he can't spend 160 minutes practicing every day. Any practice time combination that exceeds 150 minutes is not feasible. The graph's description explains that the equation 2x + 3y ≤ 15 was shaded at the bottom, while the equation x + y ≥ 3 was shaded at the top, as shown in the diagram.
2.
The graph's description explains that the equation 2x + 3y ≤ 15 was shaded at the bottom, while the equation x + y ≥ 3 was shaded at the top, as shown in the diagram.

To create and explain the graph:

Part A: The first equation of the graph was shaded at the bottom, while the top part of the shading represents the equation x + y ≥ 3.

Part B: The solutions for the equation 2x+3y<15 are (5,1). This means that when x and y are substituted with these values, the result is still less than 15.

Part C: The points on the graph represent the combination of sandwiches and hot lunches that Michael can buy within his budget for 3 students. For example, points (2,3) indicate that Michael can buy 2 sandwiches and 3 hot lunches within his budget.

You want the number of minutes Michael practices guitar and piano each day given 150 total minutes of practice and 80 more minutes practicing piano than guitar. You also want the constraints on Michael's lunch menu given he has 15 to spend on sandwiches that cost 2 and hot lunches that costs 3, provided that he gets at least 3 items.

Variables

If the problem statement does not define variables for you, then somewhere in your solution description you need to explain what each of the variables stands for.

Equations

It is helpful to say what the equations represent. Our version of your problem statements above suggests two relations for each problem. For Michael's practice time, one equation expresses the desired total, while the other expresses the desired difference.

In the lunch problem, apparently one inequality expresses the budget limit, while the other inequality expresses the item count requirement.

Graphs

In the second problem, you seem to want "to create and explain the graph." If that is the case, we expect part of your answer to explain how the graph was created and what the boundary lines and shading mean.

(The item count graph is nicely created using the x- and y-intercepts of the boundary line. The "≥" relation tells you shading is above the line. For the budget graph, the y-intercept is an integer (5), but the x-intercept is not (7.5). We're not sure how created that graph. The "≤" relation tells you shading is below the boundary line.) Since item counts and budget amounts won't be negative, only the first quadrant of the graph makes any sense in relation to the problem.

__

Additional comment

It can be useful to you, if not for the teacher, to clearly identify the sections "Given:", "Find:", "Solution:" for each problem — especially word problems. The solution space should clearly mark the solution to each part of the problem, along with showing how it was obtained.