Question

question
zoe is a high school basketball player. in a particular game, she made some free throws (worth one point each) and some two point shots. zoe made a total of 11 shots altogether and scored a total of 15 points. write a system of equations that could be used to determine the number of free throws zoe made and the number of two point shots she made. define the variables that you use to write the system.
answer attempt 1 out of 2
let
let
system of equations:

Explanation:

Step1: Define Variables

Let \( x \) = number of free throws (1 point each)
Let \( y \) = number of two - point shots

Step2: Equation for Total Shots

The total number of shots is the sum of free throws and two - point shots. Since she made 11 shots in total, we have the equation:
\( x + y=11 \)

Step3: Equation for Total Points

Free throws are worth 1 point each, so the total points from free throws is \( 1\times x=x \). Two - point shots are worth 2 points each, so the total points from two - point shots is \( 2\times y = 2y \). The total number of points is 15, so we have the equation:
\( x + 2y=15 \)

System of Equations:

The system of equations is:
\[

$$\begin{cases} x + y=11\\ x + 2y=15 \end{cases}$$

\]

Answer:

Let \( x \) = number of free throws, Let \( y \) = number of two - point shots. System of equations: \(\boldsymbol{

$$\begin{cases}x + y = 11\\x+2y=15\end{cases}$$

}\)