Question

1. halley is a high school basketball player. in a particular game, she made some three point shots and some free throws (worth one point each). halley scored a total of 14 points and made 4 times as many free throws as three point shots. which system of equations that could be used to determine the number of three point shots halley made (x) and the number of free throws she made (y)?

\\( x + 4 = y \\) and \\( 3x + y = 14

\\( 4x = y \\) and \\( 3x + y = 14

\\( x = 4y \\) and \\( x + 3y = 14

\\( x = y + 4 \\) and \\( x + 3y = 14 \\)

Explanation:

Step1: Analyze free throws and three - pointers relationship

Let \(x\) be the number of three - point shots and \(y\) be the number of free throws. We know that she made 4 times as many free throws as three - point shots. So the relationship between \(x\) and \(y\) is \(y = 4x\) (or \(4x=y\)).

Step2: Analyze the total points

Each three - point shot is worth 3 points, so the total points from three - point shots is \(3x\). Each free throw is worth 1 point, so the total points from free throws is \(y\). The total score is 14 points. So the equation for the total points is \(3x + y=14\).

Answer:

B. \(4x = y\) and \(3x + y = 14\)