Question

The Warriors scored 58 points in a recent basketball game. The team scored some 3 - point shots and some 2 - point shots. A total of 28 shots were successful. By surprise, no fouls were called so there were no 1 - point free throws were made. Write a system of equations that you would use to determine how many 3-point shots and how many 2-point shots were made.​

Answer 1

The system of equations are;

x + y = 28

2x + 3y = 58

where x is the number of two points shot and y is the number of three points shot

Overall;

There are 26 2-points shot and 2 3-points shot

Explanation:

Let the number of two points shot be x and the number of three points shot be y

Since there are a total of 28 shots with two and three points alone, then we can have;

x + y = 28. •••••••••(i)

The total number of points from 2 points shots will be 2 * x = 2x

The total number of points from 3 points shots will be 3 * y = 3y

We have the total number of points as 58;

Thus;

2x + 3y = 58 •••••••••(ii)

We can now proceed to solve this;

From i, x = 28 - y

insert this into ii

2(28-y) + 3y = 58

56 - 2y + 3y = 58

56 + y = 58

y = 58-56

y = 2

Recall;

x + y = 28

x + 2 = 28

x = 28-2

x = 26