Question

Noah is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Noah made a total of 11 shots altogether and scored a total of 29 points. Write a system of equations that could be used to determine the number of two point shots Noah made and the number of three point shots he made. Define the variables that you use to write the system.

Answer 1

Let's define the variables as follows:

- Let \( x \) be the number of two-point shots Noah made.
- Let \( y \) be the number of three-point shots Noah made.

We can set up the following system of equations based on the information given:

1. The total number of shots made:
\[
x + y = 11
\]

2. The total points scored from the shots:
\[
2x + 3y = 29
\]

Thus, the system of equations that can be used to determine the number of two-point shots and three-point shots Noah made is:

\[
\begin{cases}
x + y = 11 \\
2x + 3y = 29
\end{cases}
\]