Solve the following system of equations:?

First of all, what do the numbers in parentheses represent? Coefficients? Exponents?

Second, is the first equation supposed to be
x-15y=6(1)
or
x=15y-6(1)
or anything else? Maybe
x+15y=6(1)
or
x=15y+6(1)

You've got to clear up these confusions before anyone can help you.

x = 15y + 6 (solve by using substitution)
x = 8 - 5y

x = 15y + 6
8 - 5y = 15y + 6
15y + 5y = 8 - 6
20y = 2
y = 2/10
y = 1/10 (0.1)

x = 15y + 6
x = 15(1/10) + 6
x = 15/10 + 6
x = 3/2 + 6
x = 3/2 + 12/2
x = 15/2 (7.5)

∴ x = 15/2 (7.5) , y = 1/10 (0.1)

Should read as :-
x = 15y - 6---------(1)
x = 8 - 5y----------(2)

8 - 5y = 15y - 6
14 = 20y
y = 14/20
y = 7/10

x = 8 - 7/2
x = 9/2

x = 9/2 , y = 7/10

Check the first equation you wrote, I think it has an error. There should be a + or a - missing there, instead of one of the =.

put them in standard form
x-15y=6
x+10y=8
Multiply top by 2 and bottom by 3
2x-30y=12
3x+30y=24
5x=36
x=36/5

36/5-15y=6
multiply by 5 to get rid of fraction if you want.
36-75y=30
-75y=30
y=-30/75
y=-6/15
(36/5,-6/15)