Question

A basketball team scored a total of 97 points in a basketball game. They made a total of 42 2-point and 3-point baskets. How many 2-point baskets did they make? How many 3-point baskets did they make? Let the number of 2-point baskets = and the number of 3-point baskets =

Answer 1

29 2-point baskets were made

13 3-point baskets were made

Explanation:

Given:

x=number of 2-point baskets scored

y=number of 3-point baskets scored

First set of equations:

`2x+3y=97`

Second set of equations:

`x+y=42`

Solve for x or y in the second equation:

`x+y=42\\y=42-x`

plug in y into the first equation:

`2x+3(42-x)=97`

`2x+126-3x=97\\`

combine like terms

`x+126=97`

`x=126-97\\x=29`

So, 29 2-point baskets were made.

Now plug in 29 for x in the second equation:

`29+y=42`

subtract 29 from both sides

y=13

So, 13 3-point baskets were made.

Hope this helps! :)