System of Linear Equations Project Introduction
Systems of linear equations are a useful way to solve common problems in different areas of life. One of the most powerful ways to use them is in a comparison model where two similar situations are compared side by side to determine which one is better. In this project, you will be analyzing a real life situations using systems of linear equations to make an informed decision. The situation
1. Spending nights at a 3 star hotel in Paris, France or spending nights at a 5 star hotel in Atlanta, GA.
Vacation
Situation: You have graduated from high school and you are planning to go on a vacation by yourself. You have always wanted to travel to Paris, France, but you need to consider the price of the airplane ticket as well as the cost of the hotel per night. As an alternative, you want to look into spending the same number of nights in Atlanta at a luxurious 5 star hotel. Now you need to determine whether you should go to Paris which will cost you for flight and hotel or stay in Atlanta that will cost you only for the hotel.
Note: You are spending the same number of nights at each destination.
Project Details
For this project, you will need to: 1) Collect data.
Assignment: Gather information from travel agencies, such as American Airline, Orbitz, Expedia, or Kayak, through their website for cost of flight and cost of hotel.
Write a system of equations to represent the information you collected:
1st Equation: Cost of flight + hotel in Paris
2nd Equation: Hotel in Atlanta
Use the methods we have been studying (graphing and solving algebraically) to determine which plan is better based on the number of nights you decide to stay.

Vacation – Data Organizer (step 1 only-Please be sure to include ALL required components of the project-please refer to the Final Project Checklist and Rubric).
1) Complete the following chart to help you come up with a systems of linear
equations Destination
Hotel rating Name of hotel Price of hotel (per night) Price of flight
SOURCE OF DATE:
Paris, France

Atlanta, GA

2) Write an equation for staying in Paris, France.
3) Write an equation for staying in Atlanta, GA.
4) Define the variables (what do the variables in your equation represent) Independent Variable:
Dependent Variable:
5) Write your system of linear equation�s:

Now take your systems of equations and graph it! Be sure to label your graph and choose an appropriate scale. Show graphically what the solution to the system is and what it means about the situation.
14 points = Graphic solution
8 points = Each line is correctly graphed 2 points = Labels and titles
4 points = Point of intersection
7) Now solve your system of equations algebraically using either the substitution method or combination method. State which method you are using and why you chose that method. Show your work for how you are solving your system of equations. Explain what the solution represents in terms of the situation.
16 points = Algebraic solution and explanation
10 points = Correct solving stating what method you are using and why 2 points = Explain your work and how you came up with the parameters,
explain what the solution represents 4 points = Check solution in equations
8) Now that you have compared the two options graphically and algebraically, answer the following questions (in complete sentences).
Analysis for PART 1: Determine the answer to the following question (this is done with the graph and algebraic solution when you are using TWO variables): For how many nights are the prices going to be same?
AFTER COMPLETING PART 1 USING TWO VARAIBLES, NOW DO PART 2: If you had $1500 to spend for your vacation, which plan would you choose and why?

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