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.

Explanation:

Step1: Define variables

Let $x$ = number of free throws, $y$ = number of two-point shots

Step2: Total shots equation

Total shots = free throws + two-point shots:
$x + y = 11$

Step3: Total points equation

Total points = (1×free throws) + (2×two-point shots):
$x + 2y = 15$

Answer:

Let $x$ = number of free throws Zoe made
Let $y$ = number of two-point shots Zoe made
System of equations:
$x + y = 11$
$x + 2y = 15$