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

Let's comment the system. We can see that the first equation is
`x+y = 27`. It means that x and y are two quantities that sum to 27. Since we know that the team scored a total of 27 baskets, we know that x and y are something that "compose" the number of baskets. So, they must be the number of two and three points shot.

The second equation is
`2x + 3y = 60`. We know that the team scored 60 points, and that every x is "worth" 2 and every y is "worth" 3. So, x is the number of two-points shots and y is the number of three points shots.

To solve the system we can isolate y from the first equation:

`y = 27-x`

and substitute this expression in the second equation:

`2x + 3y = 60 \implies 2x + 3(27-x) = 60 \implies -x = -21 \implies x = 21`

So, we can deduce back

`y = 27-x = 27-21 = 6`

Now remember that x was the number of two-points shots and y was the number of three-points shots to get to the answer.

Answer 2

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

Explanation:

just did the assignment :/