This I solved years before and here the justficadtion

 In the game of basketball, each basket can be worth 1, 2 or 3 points to the team that scored the basket. The team that scores the most points wins the game.

In a particular game, Jorge “Golden Hand” made 17 baskets and scored a total of 36 points. It is also known that the number of 2-point baskets Jorge scored was three times the number of 1-point baskets he scored.

If x is the number of 1-point baskets, y is the number of 2-point baskets and z is the number of 3-point baskets scored by Jorge, then the product xyz is equal to

A) 108.

B) 120.

C) 134.

D) 135.

E) 180.

Translated with DeepL.com (free version)

Resolving again years after

1st we have that but the meaning because is the critics mathematic:

we know the value of the baskets

K - 1

L - 2

M - 3

When we work with two diferent types of incognits we could use the low case x, y, z and k, l, m

And also we can use one type in low case and the other in uppercase, when I soved I use uppercase and lower case and the normals, see K, L, M is used in the beggining because I notice that I gonna have to disappear with them to swap to x, y, z nothing about the question named like that is that I always use x, y and z, and K,L,M are temporary incognitos.

K - 1 - x

L - 2 - y

M - 3 - z

What is K, L, M the value of the baskets and x, y, z is the quantities of the basquets

So  K + L + M = 17

xK + yL + zM = 36; here K=1, L=2,M=3 -> x + 2y + 3z = 36 (1eq)

y = 3x (2eq); x + 3x + z = 17 -> 4x + z = 17 -> z = 17 - 4x (3eq)

Replacing the the 2nd and 3rd equation in the 1st equation:

x + 2*3x + 3(17 - 4x) = 36; resolving: x = 3;

Replacing the x in the 2nd and 3rd equation : y = 3*3 = 9; z = 17 - 4*3 = 5.

x*y*z = 135.

But I justify for the professor that I would replace the 3 1st incognitos for new ones.

Rute Bezerra de Menezes Gondim