Answer:
UMBC scored 10,14 and 12 one - point free throws, two point baskets and three point baskets respectively.
Step-by-step explanation:
Let's start defining the variables.
X : ''Number of 1 - point free throws''
Y : ''Number of 2 - point baskets''
Z : ''Number of 3 - point baskets''
UMBC scored a total of 74 points. Therefore,
(I)
Where X.1 represents the total points from 1 - point free throws.
Where Y.2 represents the total points from 2 - point baskets.
And finally Z.3 represents the total points from 3 - point baskets.
Reading the exercise, we can write two more equations :
![Y=Z+2\\Z=X+2](https://tex.z-dn.net/?f=Y%3DZ%2B2%5C%5CZ%3DX%2B2)
Let's write Y and X in terms of Z
(II)
⇒
(III)
Replacing (II) and (III) in (I) :
![(Z-2).1+(Z+2).2+Z.3=74](https://tex.z-dn.net/?f=%28Z-2%29.1%2B%28Z%2B2%29.2%2BZ.3%3D74)
![Z-2+2Z+4+3Z=74](https://tex.z-dn.net/?f=Z-2%2B2Z%2B4%2B3Z%3D74)
![6Z+2=74\\6Z=72\\Z=12](https://tex.z-dn.net/?f=6Z%2B2%3D74%5C%5C6Z%3D72%5C%5CZ%3D12)
We find that the variable Z is 12. Replacing this value in (II) and (III) ⇒
![Y=12+2=14\\Y=14](https://tex.z-dn.net/?f=Y%3D12%2B2%3D14%5C%5CY%3D14)
![X=12-2=10\\X=10](https://tex.z-dn.net/?f=X%3D12-2%3D10%5C%5CX%3D10)
Finally, UMBC scored 10 baskets from 1 - point free throws,14 baskets from of 2 - point and 12 baskets of 3 - point.
We can verify by replacing X = 10 , Y = 14 and Z = 12 in equation (I) :