Question

deron williams and chris paul have been compared to each other their entire careers. deron williams was drafted by the utah jazz with the third pick of the 2005 nba. chris paul was drafted one spot later by the new orleans hornets. both players have statistics from their three seasons in the league, both have played in the nba all - star, and both were part of the gold medal winning 2008 united states olympic basketball team. in basketball, a free throw is worth 1 point and a field goal is either 2 points or 3 points. in the 2007 - 2008 season, chris paul scored a total of 1684 points. the total number of 2 - point and 3 - point field goals he made was 630 and the total number of free throws he made was 332. using a system of equations, determine how many 2 - point field goals and 3 - point field goals chris paul made in the 2006 - 2007 season.

x + y = 630
2x + 3y=1684 - 332

in the 2007 - 2008 season, deron williams scored a total of 1545 points. the total number of 2 - point field goals and 3 - point field goals and free throws he made was 813 and the total number of 3 - point field goals he made was 83. using a system of equations, determine how many 2 - point field goals and free throws deron williams made in the 2006 - 2007 season.
x + y+z = 1545
x + y = 813
z = 83

Explanation:

Step1: Set up the equations

Let $x$ be the number of 2 - point field goals and $y$ be the number of 3 - point field goals. We know that the total number of 2 - point and 3 - point field goals is 630, so $x + y=630$. Also, since a free - throw is worth 1 point and he made 332 free - throws, and his total points is 1684, the points from 2 - point and 3 - point field goals is $1684 - 332\times1=1352$. So we have the equation $2x + 3y=1352$.

Step2: Solve the system of equations

From the first equation $x = 630 - y$. Substitute $x = 630 - y$ into the second equation $2(630 - y)+3y=1352$. Expand it: $1260-2y + 3y=1352$. Combine like terms: $y=1352 - 1260=92$.

Step3: Find the value of $x$

Substitute $y = 92$ into the first equation $x+y=630$, we get $x+92 = 630$, then $x=630 - 92=538$.

Answer:

The number of 2 - point field goals is 538 and the number of 3 - point field goals is 92.