Nim

I'm embarrasingly bad with math. Couldn't have solved this one without looking up the solution. =C

type Vec2 = tuple[x,y: int64]

const
  PriceA = 3
  PriceB = 1
  ErrorDelta = 10_000_000_000_000

proc isInteger(n: float): bool = n.round().almostEqual(n)
proc `+`(a: Vec2, b: int): Vec2 = (a.x + b, a.y + b)

proc solveEquation(a, b, prize: Vec2): int =
  let res_a = (prize.x*b.y - prize.y*b.x) / (a.x*b.y - a.y*b.x)
  let res_b = (a.x*prize.y - a.y*prize.x) / (a.x*b.y - a.y*b.x)
  if res_a.isInteger and res_b.isInteger:
    res_a.int * PriceA + res_b.int * PriceB
  else: 0

proc solve(input: string): AOCSolution[int, int] =
  let chunks = input.split("\n\n")
  for chunk in chunks:
    let lines = chunk.splitLines()
    let partsA = lines[0].split({' ', ',', '+'})
    let partsB = lines[1].split({' ', ',', '+'})
    let partsC = lines[2].split({' ', ',', '='})

    let a = (parseBiggestInt(partsA[3]), parseBiggestInt(partsA[6]))
    let b = (parseBiggestInt(partsB[3]), parseBiggestInt(partsB[6]))
    let c = (parseBiggestInt(partsC[2]), parseBiggestInt(partsC[5]))

    result.part1 += solveEquation(a,b,c)
    result.part2 += solveEquation(a,b,c+ErrorDelta)