Need help ASAP!

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

x be the 2-point shot and y the 3-point.

2x+3y=21

x=2y

Substituting in the first equation,

2(2y)+3y=21

y=3, x=6

Answer 2

This question is just asking for the setup, so you only need to think about how to translate the information from the prompt into individual equations.

One equation will relate to the 21 points scored and the other will cover that he made twice as many 2 point shots as 3 point shots. It does not matter whether you make the 2 point shots X or Y, as long as you are consistent. I am going to make the 2 point shots be X and the 3 point shots Y.

Since a 2 point shot is worth 2 points, 2 will be the coefficient for X in the equation with 21 as the answer. Likewise, Y will have a coefficient of 3 to capture the 3 point value. You know that Easton made some number of 2 point and 3 point shots to score 21 points. Therefore, 2X added to 3Y will represent his points scored since 2X captures the value for the 2 point shots he made, and 3Y captures the value of the 3 point shots.

So 2X+3Y=21 would be part of the system.

The other equation is just about the relation between X and Y. Since Easton made twice as many two point shots. X=2Y.

The whole system would be those two equations, and you would specify that X is the 2 point shots, and Y the 3 point shots.