Oliver is a high school basketball player. In a particular game, he made some three point shots and some two point shots. Oliver scored a total of 24 points and made 3 more three point shots than two point shots. Graphically solve a system of equations in order to determine the number of three point shots made, x, and the number of two point shots made, y.

From the graph, the two lines intersect at the point \((6, 3)\). This means:

- Oliver made **6 three-point shots** (\(x = 6\)).
- Oliver made **3 two-point shots** (\(y = 3\)).

These values satisfy both the conditions of the problem: the total points (6 three-pointers and 3 two-pointers give \(6 \times 3 + 3 \times 2 = 24\) points) and the relationship (3 more three-point shots than two-point shots).

Would you like further details or have any questions?

### 5 Related Questions:
1. How do we verify the solution algebraically instead of graphically?
2. What if Oliver made 5 more three-point shots than two-point shots? How would the system of equations change?
3. How can we solve this system using substitution or elimination methods instead of graphing?
4. What happens if Oliver scored a total of 30 points under the same conditions?
5. How would you model this problem if Oliver also made some free throws worth 1 point?

### Tip:
When solving systems of equations graphically, always look for the point of intersection—this represents the solution where both conditions are satisfied simultaneously.

Discover how to solve a system of equations graphically to find the number of three-point and two-point shots made by a high school basketball player. Learn step-by-step methods for interpreting equations in the context of a real-world problem. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation