Question

Elizabeth is a high school basketball player. In a particular game, she made some free

throws (worth one point each) and some two point shots. Elizabeth scored a total of
16 points and made twice as many free throws as two point shots. Graphically solve a
system of equations in order to determine the number of free throws made, x, and
the number of two point shots made,y. lol

Answer 1

2x / y = 16
2x because she made twice the shots with free throws then two point shots

Answer 2

Elizabeth made 8 free throws and 4 two-point shots.

Explaination:

Variable Definitions:

x= the number of free throws made

y= the number of two point shots made

Each free throw scores 1 point, so x free throws would score 1x points. Each two point shot scores 2 points, so yy two point shots would score 2y points. Therefore, the total number of points scored 1x+2y equals 16:

1x+2y=16

Since Elizabeth scored twice as many free throws as two point shots, she made more free throws, so if we multiply 2 by the number of two point shots made, we will get the number of free throws made, meaning x equals 2y.

x=2y

Write System of Equations:

​1x+2y= 16

x= 2y

Solve for y in each equation:

1x+2y=16 x=2y

2y=-1x+16 2y=x

2y/2=-1x+16/2 y=1/2x

y=-1/2x-8

The x variable represents the number of free throws made and the y variable represents the number of two point shots made. Since the lines intersect at the point (8,4) we can say:

Elizabeth made 8 free throws and 4 two-point shots.