Question

Easton is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Easton scored a total of 21 points and made twice as many two point shots as three point shots. Write a system of equations that could be used to determine the number of two point shots Easton made and the number of three point shots he made. Define the variables that you use to write the system.

Answer 1

`2x+3y=21\\x=2y`

x represents the number of two-point shots. y represent the number of three-point shots.

Explanation:

Let's let x represent the number of two-point shots Easton made and let's let y represent the number of three-point shots Easton made.

So, we know that that Easton scored a total of 21 points.

In other words, the amount of two-point shots and amount of three-point shots total 21. In an equation, this is:

`2x+3y=21`

The 2 in front of the x represents the two-point per shot, and the 3 in front of the y represents the three-point per shot.

We also know that Easton made twice as many two-point shots as three-point shots. So, we can write this as:

`x=2y`

The number of two-pointers x is equivalent to twice the number of three-pointers y.

So, our system of equations is as follows:

`2x+3y=21\\x=2y`

Notes:

To solve, use substitution. Substitute the second equation into the first:

`2(2y)+3y=21`

Multiply:

`4y+3y=21`

Combine like terms:

`7y=21`

Divide by 7:

`y=3`

Solve for x using the second equation again:

`x=2(3)=6`

So, Easton made 6 two-pointers and 3 three-pointers.