Brandon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Brandon scored a total of 16 points and made twice as many three point shots as two point shots. Write a system of equations that could be used to determine the number of two point shots Brandon made and the number of three point shots he made. Define the variables that you use to write the system.

Let's define two variables to represent the number of two-point and three-point shots Brandon made:

- Let \( x \) represent the number of two-point shots.
- Let \( y \) represent the number of three-point shots.

### Based on the problem, we can create the following system of equations:

1. **Total points equation:** Each two-point shot contributes 2 points, and each three-point shot contributes 3 points. Since Brandon scored a total of 16 points, we can write:
   \[
   2x + 3y = 16
   \]
   
2. **Relationship between the number of shots:** It is stated that Brandon made twice as many three-point shots as two-point shots, so:
   \[
   y = 2x
   \]

### System of equations:
\[
\begin{cases}
2x + 3y = 16 \\
y = 2x
\end{cases}
\]

This system can now be solved to find the number of two-point shots and three-point shots Brandon made.

Do you want me to solve the system for you? Let me know if you have any questions!

Here are some related questions for further practice:
1. What if Brandon made three times as many three-point shots as two-point shots and scored 20 points?
2. How many two-point shots and three-point shots would Brandon need to make if he scored 22 points instead?
3. If Brandon made 5 two-point shots and 4 three-point shots, what would be his total score?
4. How would the system change if he scored 18 points instead but still made twice as many three-point shots?
5. What happens to the system if Brandon scored 24 points and made equal numbers of two-point and three-point shots?

**Tip:** When solving systems of equations, substitution or elimination methods are useful. Try substituting one variable into the other equation if one variable is already expressed in terms of the other.

Learn how to set up and solve a system of equations to determine the number of two-point and three-point shots Brandon made in a basketball game. The problem involves algebraic concepts such as linear equations and systems of equations. Perfect for students in Grades 8-10.

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