Question

In your basketball game, you only made 2-point and 3-point shots. You made a total of 10 shots and scored a total of 22 points. Write and solve a system of linear equations to determine how many of your shots were two-pointers and how many were 3-pointers.

a) 6 two-pointers and 4 three-pointers
b) 5 two-pointers and 5 three-pointers
c) 7 two-pointers and 3 three-pointers
d) 8 two-pointers and 2 three-pointers

Answer 1

By setting up and solving a system of linear equations, the player made 8 two-pointers and 2 three-pointers to achieve a total of 10 shots and 22 points.

Step-by-step explanation:

To determine how many 2-pointers and 3-pointers were made in a basketball game where a total of 10 shots were made and 22 points were scored, we can set up a system of linear equations. Let x represent the number of 2-pointers and y represent the number of 3-pointers. Using the given information, we have two equations:

• Equation 1: x + y = 10 (since the total number of shots is 10)
• Equation 2: 2x + 3y = 22 (since the total points scored from 2-pointers and 3-pointers is 22)

To solve this system, we can use substitution or elimination. Using substitution, solve Equation 1 for y:

y = 10 - x

Now substitute y from Equation 1 into Equation 2:

2x + 3(10 - x) = 22

Simplify and solve for x:

2x + 30 - 3x = 22

-x = -8

x = 8

Substitute x back into Equation 1 to find y:

y = 10 - 8 = 2

The player made 8 two-pointers and 2 three-pointers.