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The problem in the image you've shared describes a football game where there were 13 scoring plays, including touchdowns, extra points, and field goals, and the total score was 96 points. It asks to set up a system of equations to determine the number of touchdowns, extra points, and field goals.

Let’s break this down step by step and create the system of equations based on the information provided:

### Variables:
- Let **x** represent the number of touchdowns (each worth 6 points).
- Let **y** represent the number of extra points (each worth 1 point).
- Let **z** represent the number of field goals (each worth 3 points).

### Given conditions:
1. There were 13 scoring plays in total. This gives the equation:
   \[
   x + y + z = 13
   \]
   
2. The total score was 96 points. This gives the equation:
   \[
   6x + y + 3z = 96
   \]
   
3. There were twice as many touchdowns as field goals. This gives the equation:
   \[
   x = 2z
   \]

### System of Equations:
Now, the system of equations is:
1. \( x + y + z = 13 \)
2. \( 6x + y + 3z = 96 \)
3. \( x = 2z \)

We can solve this system to find the values of \(x\), \(y\), and \(z\).

Let me know if you would like me to proceed with solving it, or if you have any questions!

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Here are 5 related questions:
1. What would happen if the total points were different but the number of scoring plays remained the same?
2. How would the system change if touchdowns were worth 7 points instead of 6?
3. Can you generalize this system for any number of touchdowns, extra points, and field goals?
4. What if there were more types of scoring plays, such as a safety, worth 2 points?
5. How can you check whether a given set of scores is possible given certain conditions?

**Tip**: When setting up a system of equations, always define your variables clearly and identify how many relationships you need to solve them accurately!

In a football game, there were 13 scoring plays. These plays were a combination of touchdowns (6 points), extra-point kicks (1 point), and field goals (3 points). There were twice as many touchdowns as field goals. There were 96 points earned from the field goals, extra points, and touchdowns combined. Formulate a system of equations that could be used to determine the number of touchdowns, extra points, and field goals that were scored during the game.

Learn how to formulate and solve a system of equations based on a football game scenario with 13 scoring plays including touchdowns, extra points, and field goals, totaling 96 points. This guide covers the essential algebraic concepts and provides a step-by-step approach, suitable for Grades 9-10.

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