Landon is a high school basketball player. In a particular game, he made some two-point shots and some three-point shots. Landon scored a total of 24 points and made 2 more two-poi... Landon is a high school basketball player. In a particular game, he made some two-point shots and some three-point shots. Landon scored a total of 24 points and made 2 more two-point shots than three-point shots. Graphically solve a system of equations to determine the number of two-point shots made, x, and the number of three-point shots made, y.
Understand the Problem
The question is asking to use a system of equations to determine the number of two-point shots made by Landon, given that he scored a total of 24 points and made 2 more two-point shots than three-point shots. The user is required to graphically solve this system of equations.
Answer
Landon made $6$ two-point shots and $4$ three-point shots.
Answer for screen readers
Landon made 6 two-point shots and 4 three-point shots.
Steps to Solve
-
Define Variables Let $x$ be the number of three-point shots made, and $y$ be the number of two-point shots made.
-
Set Up Equations From the problem, there are two key facts:
- The total points scored is 24: $$ 2y + 3x = 24 $$
- The number of two-point shots is 2 more than the number of three-point shots: $$ y = x + 2 $$
-
Substitute Substitute the second equation into the first:
- Replace $y$ with $x + 2$ in the total points equation: $$ 2(x + 2) + 3x = 24 $$
-
Simplify the Equation Distributing and combining like terms:
- Expand the equation: $$ 2x + 4 + 3x = 24 $$
- Combine like terms: $$ 5x + 4 = 24 $$
-
Solve for $x$ Subtract 4 from both sides: $$ 5x = 20 $$ Now, divide by 5: $$ x = 4 $$
-
Find $y$ Use the value of $x$ to find $y$ using the second equation: $$ y = x + 2 = 4 + 2 = 6 $$
Landon made 6 two-point shots and 4 three-point shots.
More Information
Landon's points contribute as follows: each two-point shot gives him 2 points, and each three-point shot gives him 3 points. Thus, from 6 two-point shots, he scores $6 \times 2 = 12$ points, and from 4 three-point shots, he scores $4 \times 3 = 12$ points, totaling 24 points.
Tips
- Failing to substitute correctly can lead to incorrect equations. Always check that you've substituted into the correct equation.
- Miscalculating the total points when combining the contributions from two- and three-point shots is common. Double-checking the math can prevent errors.
AI-generated content may contain errors. Please verify critical information
