In a​ state's Pick 3 lottery​ game, you pay ​$1.14 to select a sequence of three digits​ (from 0 to​ 9), such as 377. If you select the same sequence of three digits that are​ drawn, you win and collect ​$363.99. How many different selections are​ possible?

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.