function gauss(a){
  let arr = a.map(r => r.slice());
  let [n, m] = [arr.length, arr[0].length];
  let [h, k] = [0, 0];
  while(h < n && k < m){
    let idx = h;
    while(idx < n && arr[idx][k] == 0) idx++;
    if(arr[idx][k] == 0){
      k++;
    } else {
      [arr[idx], arr[h]] = [arr[h], arr[idx]];
      for(let i = h + 1; i < n; i++){
        const f = arr[i][k] / arr[h][k];
        arr[i][k] = 0;
        for(let j = k + 1; j < m; j++){
          arr[i][j] -= arr[h][j] * f;
        }
      } 
    h++;
    k++;
    }
  }
  return arr;
}

function solve(a){
  let [n, m] = [a.length, a[0].length];
  const arr = gauss(a);
  let sol = Array(n).fill(null);
  sol[n - 1] = arr[n - 1][m - 1] / arr[n - 1][m - 2];
  for(let i = n - 2; i > -1; i--){
    let sum = 0;
    for(let j = i + 1; j < n; j++){
      sum += arr[i][j] * sol[j];
    }
    sol[i] = (arr[i][m - 1] - sum) / arr[i][i];
  }
  return sol;
}

function gaussSolve(a, b){
  let arr = a.map(r => r.slice());
  for (let i = 0; i < arr.length; i++){
    arr[i].push(b[i]);
  } 
  const sol = solve(arr);
  return sol
}

let  a = [[1, 1, 1, 0], [1, 1, 0, 1], [1, 0, 1, 1], [0, 1, 1, 1]]
let b = [1, -1, 2, 3]
let x = gaussSolve(a, b)
console.log("x: ", x)