Answer:
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.
