# In basketball, a free throw is 1 point and a field goal is either 2 or 3 points. In a recent season, Tim Duncan of the San Antonio Spurs scored a total of 1342 points. The total number of 2-point field goals and 3-point field goals was 517, and he made 305 of the 455 free throws that he attempted. Find the nu,ber of 2-point field goals and 3-point field goals Duncan made that season.

I just need to know the two equations and then I can solve it.

## let the number of 2-pointers be x

let the number of 3-pointers be y

x+y = 517

2x + 3y + 305 = 1342

I got 514 2-pointers, only 3 3-pointers, and 305 free throws.

These answers check out, but must be false data, only 3 threepointers per season would be pretty poor shooting.

## The data for Tim Duncan are probably correct. He plays center most of the time, and occasionally plays power forward. In these positions, he very seldom gets a chance to shoot from beyond the three point line, and probably would not want to if he did. So far in the 2007-2008 season, he has taken only one three-point shot, and missed it.

## 5x=3y+567

## To solve for the number of 2-point and 3-point field goals made by Tim Duncan, we can set up two equations.

Let's say the number of 2-point field goals made by Duncan is 'x', and the number of 3-point field goals made by Duncan is 'y'.

1. The first equation represents the total points scored by Tim Duncan:

2x + 3y (points from field goals) + 305 (points from free throws) = 1342

This equation accounts for the total points scored by Duncan in a season, including both field goals and free throws.

2. The second equation represents the total number of field goals made by Duncan:

x (2-point field goals) + y (3-point field goals) = 517

This equation accounts for the total number of field goals made by Duncan, including both 2-point and 3-point shots.

Now you can solve this system of equations to find the values of 'x' and 'y'.