func gaussEliminate(_ sys: [[Double]]) -> [Double]? {
  var system = sys

  let size = system.count

  for i in 0..<size-1 where system[i][i]!= 0 {
    for j in i..<size-1 {
      let factor = system[j + 1][i] / system[i][i]

      for k in i..<size+1 {
        system[j + 1][k] -= factor * system[i][k]
      }
    }
  }

  for i in (1..<size).reversed() where system[i][i]!= 0 {
    for j in (1..<i+1).reversed() {
      let factor = system[j - 1][i] / system[i][i]

      for k in (0..<size+1).reversed() {
        system[j - 1][k] -= factor * system[i][k]
      }
    }
  }

  var solutions = [Double]()

  for i in 0..<size {
    guard system[i][i]!= 0 else {
      return nil
    }

    system[i][size] /= system[i][i]
    system[i][i] = 1
    solutions.append(system[i][size])
  }

  return solutions
}

let sys = [
  [1.00, 0.00, 0.00, 0.00, 0.00, 0.00, -0.01],
  [1.00, 0.63, 0.39, 0.25, 0.16, 0.10, 0.61],
  [1.00, 1.26, 1.58, 1.98, 2.49, 3.13, 0.91],
  [1.00, 1.88, 3.55, 6.70, 12.62, 23.80, 0.99],
  [1.00, 2.51, 6.32, 15.88, 39.90, 100.28, 0.60],
  [1.00, 3.14, 9.87, 31.01, 97.41, 306.02, 0.02]
]

guard let sols = gaussEliminate(sys) else {
  fatalError("No solutions")
}

for (i, f) in sols.enumerated() {
  print("X\(i + 1) = \(f)")
}