MATH: Can you please check my work (vectors - grade 12)

Q: If 2x + 3y = a and -x + 5y = 6b, express x and y in terms of a and b.
My answer:
x = a/2 - 3y/2
y = 6b/5 + x/5
Rearrange and sub
y = (1/13)a + (12/13)b --> matches answer key

x = (1/2)a - (3/2)y
= (1/2)a - (3/2)(6b/5 + x/5)
x = (5/7)a - (18/7)b --> wrong according to the answer key,
the right answer -> x = (5/13)a - (18/13)b

Did I do something wrong or is the answer key mistaken?

I'll show you my way, and you can compare yours AND the key
Multiply the second equation by 2, then add the two equations.
+2x+3y=a
-2x+10y=12b
-------------------
13y=a+12b
y=(a+12b)/13 This does agree with you and the answer key

Substitute into the first equation as you did
x = (a-3y)/2 = a/2 -(3/2)y Agrees with you
x = a/2 - (3/2)((a+12b)/13)
x = a/2 - 3a/(2*13) - 3*12*b/(2*13)
x = 13a/26 - 3a/26 - 18b/13
x = 10a/26 - 18b/13
x = 5a/13 - 18b/13 Agrees with key; Sorry