Will someone me answer this

luca and william are playing a video game and they have scored a total of 20,000 points. luca scored 4,000 more points than william. if you let l= the number of points that luca scored, and w= the number of points that william scored, then the problem can be represented by the system:

l+w=20,000 and l=w+4,000

graph the system. how many points did each boy score?

my possible answers are:
a. william = 8,000 and luca = 12,000
b. william = 12,000 and luca = 8,000

d. william = 4,000 and luca = 16,000

l+w=20000

l=w+4000

w+4000+w=20000

2w+4000=20000

2w=16000

w=8000

l = 8000 +4000 = 12000

William scored 8000, Luca scored 12000

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

b). 4320 have a nice day