On march 9, 2018, ncaa fans across the world were shocked when the retrievers of the university of maryland, baltimore county (umbc) upset the virginia cavaliers. umbc scored a total of 74 points resulting from a combination of 3-point baskets, 2-point baskets, and 1-point free throws. there were 2 more 2-point baskets than 3-point baskets and 2 more 3-point baskets than 1-point free throws.

a) set up a system of linear equations to find the number of three-point baskets, two-point baskets, and one-point free-throws. (label your variables)

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 :

Let's write Y and X in terms of Z

(II)

⇒ (III)

Replacing (II) and (III) in (I) :

We find that the variable Z is 12. Replacing this value in (II) and (III) ⇒

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) :

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