Could anyone help with this ASAP ?? tyy! Answer the following questions using what you've learned from this unit. Write your responses in the space provided.
1. Solve the system of equations, first by graphing, and then algebraically. (8 points)
y = x – 2 and y = –2x + 7
Part I: Graph the two equations and label the point where they cross. (3 points)

Part II: If f(x) = x – 2 and g(x) = –2x + 7, what value of x makes f(x) = g(x)? (1 point)

Part III: Use the substitution method to solve the system of equations. Write your answer as an ordered pair. (4 points)
y = x – 2 and y = –2x + 7

2. A ski lodge offers two weekend packages. Package A provides 2 nights and 3 meals for $280. Package B provides 2 nights and 5 meals for $320. Write and solve a system of equations to find the costs per night and per meal. (Assume the cost per night and cost per meal are the same for both packages.) Use n to represent the cost per night and m to represent the cost of each meal. (8 points)
Step 1: The equation representing package A is given. Complete the system of equations by writing an equation to represent package B. (1 point)

Package A: 2n + 3m = 280
Package B:

Step 2: Select a method for solving the system. Which method did you choose? Why? (2 points)

Step 3: Solve the system of equations to find the costs per night and per meal. Show your work.(3 points)

Step 4: Explain the meaning of the solutions for m and n. (2 points: 1 point each)

3. Given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solution. Show why this is true by solving the system of equations given. Justify the reason for each step. HINT: Use addition property of equality and multiplication property of equality in your answers. (8 points: 1 point for each question)
5x + 2y = 7
3x – y = 2
To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations. (1 point)

Why is this multiplication allowed? (1 point)

What variable will be eliminated when the equations are combined after the multiplication? (1 point)

Next, add the equations together. Your answer should be a single equation with one variable. (1 point)

Why can you add the equations? (1 point)

Solve the equation for x. (1 point)

Substitute x back into one of the equations to solve for y. (1 point)

What is the solution to the system of equations? (1 point)

4. Solve the system of equations. (6 points)

Part I: Explain the steps you would take to solve the system by eliminating the x-terms. (1 point)

Part II: Explain the steps you would take to solve the system by eliminating the y-terms. (2 points)

Part III: Choose either of the methods described in parts I or II to solve the system of equations. Write your answer as an ordered pair. Show your work. (3 points)

5. Approximate the solution to this system of equations. (6 points)
y = –x + 3
y = 2x + 1
The first step is to identify y-values for different values of x. The table showsy-values for the two functions between x = –1 and x = 2.

xy = –x + 3y = 2x + 1
–14–1
–0.53.50
031
0.52.52
123
1.51.54
215
How do you know that the solution is between the two highlighted rows? (1 point)

Complete the table to show the values of x between 0.5 and 1. (2 points)

xy = –x + 3y = 2x + 1
0.52.52
0.6
0.7
0.8
0.9
123
Which two x-values will the solution be between? (1 point)

Identify a reasonable approximation for the solution of this system. (2 points)

6. Find the solution to a system of inequalities. (6 points)
Graph this system of inequalities. Identify the solution region on the graph. (5 points: 2 points for boundary lines, 2 points for shading, 1 point for identifying the solution)

y < –x + 4
y > –x – 2

How many solutions does this system of inequalities have? (1 point)

7. The pep club and honor society are joining forces to raise money for school improvements. Together they hope to raise at least $500. The pep club is holding a raffle that will raise at least $100. The system of inequalities representing this situation is

x + y ≥ 500
x ≥ 100

where x represents pep club donations and y represents donations raised by the honor society.(8 points)
Graph this system of inequalities. (4 points)

What does the point (300, 100) represent? Is it a viable solution? Why or why not? (2 points)

What does the point (500, 200) represent? Is it a viable solution? Why or why not? (2 points)