Question

Layla is a high school basketball player. In a particular game, she made some three-point shots and some two-point shots. Layla scored a total of 24 points and made twice as many three-point shots as two-point shots. Graphically solve a system of equations to determine the number of three-point shots made (x) and the number of two-point shots made (y).

A) (12, 6)
B) (8, 4)
C) (6, 12)
D) (4, 8)

Answer 1

To determine the number of three-point shots made (x) and the number of two-point shots made (y), we can solve a system of equations. From the given information, we have the equations x + y = 24 and x = 2y. By substituting the value of y back into x, we find that the number of three-point shots is 16 and the number of two-point shots is 8.

Step-by-step explanation:

Let's use a system of equations to represent the information given. Let x represent the number of three-point shots made, and let y represent the number of two-point shots made.

From the given information, we have the following two equations:

• x + y = 24 (Equation 1)
• x = 2y (Equation 2)

We can solve this system of equations by substituting Equation 2 into Equation 1:

2y + y = 24

3y = 24

y = 8

Substituting this value of y back into Equation 2:

x = 2(8)

x = 16

Therefore, the number of three-point shots made is 16, and the number of two-point shots made is 8. So, the correct answer is (16, 8) (D).