Question

At a basketball​ game, a team made 59 successful shots. They were a combination of​ 1- and​ 2-point shots. The team scored 99 points in all. Write and solve a system of equations to find the number of each type of shot.

Answer 1

Explanation:

Let x be the number of 1-point shots and y be the number of 2-point shots. We know that the total number of shots is 59 and the total number of points is 99. We can write these two equations as follows:

x + y = 59

1x + 2y = 99

To solve this system of equations, we can use substitution. We can solve the first equation for y and substitute the result into the second equation:

y = 59 - x

1x + 2(59 - x) = 99

1x + 118 - 2x = 99

-x = -19

x = 19

Now that we know the value of x, we can substitute it into the first equation to find the value of y:

y = 59 - 19 = 40
Therefore, the team made 19 1-point shots and 40 2-point shots.

Answer 2

Answer: 19 one-point shots and 40 two-point shots

Explanation:

We will create a system of equations as directed to solve.

We will create one for the number of shots. Let x be one-point shots and y be two-point shots. Next, we will create one for total points. This gives us our system.

x + y = 59

x + 2y = 99

We will transform one of the equations to be equal to one of the variables.

x + y = 59 ➜ x = 59 - y

Then, we can substitute this back into the other equation to solve.

(59 - y) + 2y = 99

59 + y = 99

y = 40 two-point shots

Lastly, we will substitute this value back into the original equation to solve for the number of one-point shots.

x + y = 59

x + 40 = 59

x = 19 one-point shots