Question
Writing and Solving a System of Equations Using a Graphing Calculator
PROCEDURE
1. Write a system of equations to
the given scenario.
2. Graph the system using the calculator.
3. Adjust the window to locate where the lines intersect.
4. L the solution for the scenario.
Solving a Linear System Using a Graphing Calculator
REAL-WORLD CONNECTION
The East Side High Wild Dogs basketball team has special student pricing for tickets to their home games. Groups of 3 or more students pay an initial fee of $3, and then pay $2 for each ticket. The West Side High Rattlers basketball team also offers special student pricing for home games. At West Side, groups of 3 or more students pay an initial fee of $6, and then pay $1.75 for each ticket.
x number of students
Write a system of equations to represent the scenario.
y=2x+
y=1.75x+
PROCEDURE
1. Write a system of equations to
the given scenario.
2. Graph the system using the calculator.
3. Adjust the window to locate where the lines intersect.
4. L the solution for the scenario.
Solving a Linear System Using a Graphing Calculator
REAL-WORLD CONNECTION
The East Side High Wild Dogs basketball team has special student pricing for tickets to their home games. Groups of 3 or more students pay an initial fee of $3, and then pay $2 for each ticket. The West Side High Rattlers basketball team also offers special student pricing for home games. At West Side, groups of 3 or more students pay an initial fee of $6, and then pay $1.75 for each ticket.
x number of students
Write a system of equations to represent the scenario.
y=2x+
y=1.75x+
Answers
GPT-4o mini
To write a system of equations representing the ticket pricing for the basketball games at East Side High and West Side High, we will define the following variables:
- Let \( x \) represent the number of tickets purchased (which also corresponds to the number of students, since each student buys one ticket).
- Let \( y \) represent the total cost of tickets.
Based on the problem description, we can create the following equations for each team:
1. **East Side High Wild Dogs:**
- For groups of 3 or more students, the total cost is represented by an initial fee of $3 plus $2 for each ticket purchased.
- Therefore, the equation for East Side is:
\[
y = 2x + 3
\]
2. **West Side High Rattlers:**
- For groups of 3 or more students, the total cost is represented by an initial fee of $6 plus $1.75 for each ticket purchased.
- Hence, the equation for West Side is:
\[
y = 1.75x + 6
\]
Now we have a system of equations:
\[
\begin{align*}
y &= 2x + 3 \quad \text{(East Side High)} \\
y &= 1.75x + 6 \quad \text{(West Side High)}
\end{align*}
\]
### Steps to Graph the System and Find the Intersection
1. **Graph the Equations:**
- Use a graphing calculator to input the two equations:
```
y = 2x + 3
y = 1.75x + 6
```
2. **Adjust the Window:**
- Choose an appropriate window size to catch both equations. A suggestion for the window might be:
- Xmin = 0
- Xmax = 10
- Ymin = 0
- Ymax = 20
3. **Locate the Intersection:**
- Use the graphing calculator's "Intersect" feature to find the point where the two lines meet.
4. **Read the Solution:**
- The intersection point will give the values of \( x \) (number of tickets/students) and \( y \) (total cost).
- Once you find the intersection, you can determine how many tickets (students) can be bought at both prices for the same total cost.
In this case, you would find the intersection point, which represents the number of students where both teams charge the same amount for tickets. This provides insight into pricing strategies and can help students choose which game to attend based on cost.
- Let \( x \) represent the number of tickets purchased (which also corresponds to the number of students, since each student buys one ticket).
- Let \( y \) represent the total cost of tickets.
Based on the problem description, we can create the following equations for each team:
1. **East Side High Wild Dogs:**
- For groups of 3 or more students, the total cost is represented by an initial fee of $3 plus $2 for each ticket purchased.
- Therefore, the equation for East Side is:
\[
y = 2x + 3
\]
2. **West Side High Rattlers:**
- For groups of 3 or more students, the total cost is represented by an initial fee of $6 plus $1.75 for each ticket purchased.
- Hence, the equation for West Side is:
\[
y = 1.75x + 6
\]
Now we have a system of equations:
\[
\begin{align*}
y &= 2x + 3 \quad \text{(East Side High)} \\
y &= 1.75x + 6 \quad \text{(West Side High)}
\end{align*}
\]
### Steps to Graph the System and Find the Intersection
1. **Graph the Equations:**
- Use a graphing calculator to input the two equations:
```
y = 2x + 3
y = 1.75x + 6
```
2. **Adjust the Window:**
- Choose an appropriate window size to catch both equations. A suggestion for the window might be:
- Xmin = 0
- Xmax = 10
- Ymin = 0
- Ymax = 20
3. **Locate the Intersection:**
- Use the graphing calculator's "Intersect" feature to find the point where the two lines meet.
4. **Read the Solution:**
- The intersection point will give the values of \( x \) (number of tickets/students) and \( y \) (total cost).
- Once you find the intersection, you can determine how many tickets (students) can be bought at both prices for the same total cost.
In this case, you would find the intersection point, which represents the number of students where both teams charge the same amount for tickets. This provides insight into pricing strategies and can help students choose which game to attend based on cost.