Question

1. hailey is a high school basketball player. in a particular game, she made some three point shots and some free throws (worth one point each). hailey 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 hailey made (x) and the number of free throws she made (y)?

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

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

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

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

Explanation:

Step1: Analyze free throws and three-pointers relation

Hailey made 4 times as many free throws (\(y\)) as three - point shots (\(x\)), so \(y = 4x\) (or \(4x=y\)).

Step2: Analyze total points

Three - point shots are worth 3 points each, so points from three - point shots are \(3x\). Free throws are worth 1 point each, so points from free throws are \(y\). Total points are 14, so \(3x + y=14\).

Answer:

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