Question

Write the system of linear equations and a word problem once the data has been collected. (Graphing and solving algebraically) to find the solution to the written system.

Flights to Paris: $2,506

3-star hotel in Paris per night: $79

5-star hotel in Atlanta per night: $109

7-day stay in Atlanta: $763

7-day stay in Paris + flight: $3,059

a. Determine the number of nights stayed in Paris.

b. Find the cost per night for the 3-star hotel in Paris.

c. Calculate the cost of the flight to Paris.

d. Determine the total cost of the 7-day stay in Atlanta.

Answer 1

To find the solution to the system of linear equations, set up equations using the given information and solve using graphing or algebraic methods.

Step-by-step explanation:

To find the solution to the system of linear equations, we can set up equations using the given information. Let's define the variables:

x: number of nights stayed in Paris

y: cost per night for the 3-star hotel in Paris

z: cost of the flight to Paris

From the given information, we can set up the following equations:

Equation 1: 3-star hotel cost + flight cost = 7-day stay in Paris + flight cost

79x + z = 3059

Equation 2: 5-star hotel cost + 7-day stay in Atlanta cost = 7-day stay in Atlanta + flight cost

109z + 763 = z + 2506

To solve this system of equations, we can use graphing or algebraic methods. Graphing involves plotting the equations on a graph and finding the point of intersection, which represents the solution. Algebraically, we can solve the system by substitution or elimination.