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Write a system of equations to model this situation, where xrepresents the number of years since 2014.

Write a system of equations to model this situation, where xrepresents the number of years since 2014.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Problem Statement **North Babylon High School had four members on their cross country team in 2014. Over the next several years, the team increased by an average of 6 members per year. The same school had 16 members in their orchestra in 2014. The orchestra saw an increase of 4 members per year.** **Write a system of equations to model this situation, where `x` represents the number of years since 2014.** ### System of Equations To represent this problem with a system of equations, we'll define the number of members in the cross country team and the orchestra team as functions of the number of years since 2014 (`x`). 1. Let \( y_1 \) be the number of cross country team members `x` years since 2014. - Initial members in 2014: 4 - Increase per year: 6 - Equation: \( y_1 = 4 + 6x \) 2. Let \( y_2 \) be the number of orchestra members `x` years since 2014. - Initial members in 2014: 16 - Increase per year: 4 - Equation: \( y_2 = 16 + 4x \) ### Graphing the System of Equations Below is a blank graph on which you can plot these linear equations to visually compare the growth of the two teams over the years: ![Graph](graph.png) - **X-axis**: Represents the number of years since 2014 (`x`). - **Y-axis**: Represents the number of members (in either the cross country team or the orchestra). ### Instructions for Plotting 1. Start by plotting the initial points for both teams: - For the cross country team: (0, 4) - For the orchestra: (0, 16) 2. Use the slopes of the equations to plot more points: - For the cross country team (slope = 6): Go up 6 units for every 1 unit you move to the right. - For the orchestra (slope = 4): Go up 4 units for every 1 unit you move to the right. 3. Draw the lines through the points for each team to complete the graph. By comparing the lines on the graph, you will be able to analyze and visualize the growth
Transcribed Image Text:### Problem Statement **North Babylon High School had four members on their cross country team in 2014. Over the next several years, the team increased by an average of 6 members per year. The same school had 16 members in their orchestra in 2014. The orchestra saw an increase of 4 members per year.** **Write a system of equations to model this situation, where `x` represents the number of years since 2014.** ### System of Equations To represent this problem with a system of equations, we'll define the number of members in the cross country team and the orchestra team as functions of the number of years since 2014 (`x`). 1. Let \( y_1 \) be the number of cross country team members `x` years since 2014. - Initial members in 2014: 4 - Increase per year: 6 - Equation: \( y_1 = 4 + 6x \) 2. Let \( y_2 \) be the number of orchestra members `x` years since 2014. - Initial members in 2014: 16 - Increase per year: 4 - Equation: \( y_2 = 16 + 4x \) ### Graphing the System of Equations Below is a blank graph on which you can plot these linear equations to visually compare the growth of the two teams over the years: ![Graph](graph.png) - **X-axis**: Represents the number of years since 2014 (`x`). - **Y-axis**: Represents the number of members (in either the cross country team or the orchestra). ### Instructions for Plotting 1. Start by plotting the initial points for both teams: - For the cross country team: (0, 4) - For the orchestra: (0, 16) 2. Use the slopes of the equations to plot more points: - For the cross country team (slope = 6): Go up 6 units for every 1 unit you move to the right. - For the orchestra (slope = 4): Go up 4 units for every 1 unit you move to the right. 3. Draw the lines through the points for each team to complete the graph. By comparing the lines on the graph, you will be able to analyze and visualize the growth
**Question:** Explain in detail what each coordinate of the point of intersection of these equations means in the context of this problem.
Transcribed Image Text:**Question:** Explain in detail what each coordinate of the point of intersection of these equations means in the context of this problem.
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