How many gold rings did they sell? God bless! Please include an explanation if possible! Thanks!

First subtract 10 from both side
y^2+6y-16=0
(y+8)(y-2)=0
-8 and 2

Ibelieve it is 5,040

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.