Help with a word problem (using a system of equations and elimination)

Use a system of equations and elimination to solve this problem:

Anita is 4.5 years older than Basilio. Three times Anita's age added to six times Basilio's age is 36. How old are Anita and Basilio?

A = Anita's age
B = Basilio's age

A = B + 4.5
3A + 6B = 36

A-B = 4.5
3A + 6B = 36

-3A+3B= -13.5
3A + 6B = 36

add them...
9B = 22.5
B = 2.5

A=B+4.5
A=2.5+4.5
A=7

let Basillo = B and Anita = A

A = B+4.5
therefore B = A - 4.5

3A + 6B = 36
(now substitute A = B+4.5 into this equation to get Basilios age)
3(B+4.5) + 6B = 36
3B+13.5+6B = 36
9B = 22.5
therefore B = 2.5 Basilio is 2.5years old

then substitute B = 2.5 into 3A+6B = 36 to get Anitas age or substitute B=A-4.5
you should get the same answer (you can use the 2nd method as a check to see if you correct)
A = 7