Question

A high school basketball team scored 60 points in last week’s game. The team scored a total of 27 baskets; some were two-point shots and some were three-point shots. How many two-point shots did they make? How many three-point shots did they make?

x + y = 27,

2x + 3y = 60

What is the solution of the system of equations, and what does it represent?
(6, 21); 6 two-point shots and 21 three-point shots
(6, 21); 6 three-point shots and 21 two-point shots
(21, 6); 21 two-point shots and 6 three-point shots
(21, 6); 21 three-point shots and 6 two-point shots

Answer 1

To solve the system of equations given:

1. \( x + y = 27 \) (where \( x \) is the number of two-point shots, and \( y \) is the number of three-point shots)
2. \( 2x + 3y = 60 \)

We will use substitution or elimination. Here, we'll use the substitution method.

From the first equation, we can express \( y \) in terms of \( x \):

\[
y = 27 - x
\]

Now, substitute \( y \) in the second equation:

\[
2x + 3(27 - x) = 60
\]

Distributing the 3:

\[
2x + 81 - 3x = 60
\]

Combine like terms:

\[
- x + 81 = 60
\]

Now, isolate \( x \):

\[
- x = 60 - 81
\]
\[
- x = -21
\]
\[
x = 21
\]

Now, substitute \( x = 21 \) back into the equation \( y = 27 - x \):

\[
y = 27 - 21 = 6
\]

So, we have \( x = 21 \) (two-point shots) and \( y = 6 \) (three-point shots).

Thus, the solution of the system of equations is:

\[
(x, y) = (21, 6)
\]

This means the team made **21 two-point shots** and **6 three-point shots**.

The correct interpretation from the provided options is:

**(21, 6); 21 two-point shots and 6 three-point shots.**