


"""simple docstring"""


def  __snake_case       (   UpperCamelCase__	)      ->		list[list]:







		"""simple docstring"""





		A					       = current_set.copy()
		for row_index, row in enumerate(_lowerCamelCase	):
				A					       = row[0]
				for column_index, column in enumerate(_lowerCamelCase	):
						if magnitude == 0:
								A					       = column
								continue
						A					       = column / magnitude
    # Subtract to cancel term
		A					       = current_set[0]
		A					       = [first_row]
		A					       = current_set[1::]
		for row in current_set:
				A					       = []
				# If first term is 0, it is already in form we want, so we preserve it
				if row[0] == 0:
						final_set.append(_lowerCamelCase	)
						continue
				for column_index in range(len(_lowerCamelCase	)	):
						temp_row.append(first_row[column_index] - row[column_index]	)
				final_set.append(_lowerCamelCase	)
		# Create next recursion iteration set
		if len(final_set[0]	) != 3:
				A					       = final_set[0]
				A					       = []
				A					       = []
				for row in final_set[1::]:
						current_first_column.append(row[0]	)
						next_iteration.append(row[1::]	)
				A					       = simplify(_lowerCamelCase	)
				for i in range(len(_lowerCamelCase	)	):
						resultant[i].insert(0 ,			current_first_column[i]	)
				resultant.insert(0 ,			_lowerCamelCase	)
				A					       = resultant
		return final_set







def  __snake_case       (   UpperCamelCase__	)      ->		list:







		"""simple docstring"""





		if len(_lowerCamelCase	) == 0:
				raise IndexError('solve_simultaneous() requires n lists of length n+1'	)
		A					       = len(_lowerCamelCase	) + 1
		if any(len(_lowerCamelCase	) != _length for item in equations	):
				raise IndexError('solve_simultaneous() requires n lists of length n+1'	)
		for row in equations:
				if any(not isinstance(_lowerCamelCase ,			(int, float)	) for column in row	):
						raise ValueError('solve_simultaneous() requires lists of integers'	)
		if len(_lowerCamelCase	) == 1:
				return [equations[0][-1] / equations[0][0]]
		A					       = equations.copy()
		if any(0 in row for row in data_set	):
				A					       = data_set.copy()
				A					       = []
				for row_index, row in enumerate(_lowerCamelCase	):
						if 0 not in row:
								A					       = data_set.pop(_lowerCamelCase	)
								break
				if not full_row:
						raise ValueError('solve_simultaneous() requires at least 1 full equation'	)
				data_set.insert(0 ,			_lowerCamelCase	)
		A					       = data_set.copy()
		A					       = simplify(_lowerCamelCase	)
		A					       = simplified[::-1]
		A					       = []
		for row in simplified:
				A					       = row[-1]
				if not solutions:
						if row[-2] == 0:
								solutions.append(0	)
								continue
						solutions.append(current_solution / row[-2]	)
						continue
				A					       = row.copy()[: len(_lowerCamelCase	) - 1 :]
				while temp_row[0] == 0:
						temp_row.pop(0	)
				if len(_lowerCamelCase	) == 0:
						solutions.append(0	)
						continue
				A					       = temp_row[1::]
				A					       = temp_row[::-1]
				for column_index, column in enumerate(_lowerCamelCase	):
						current_solution -= column * solutions[column_index]
				solutions.append(_lowerCamelCase	)
		A					       = []
		for item in solutions:
				final.append(float(round(_lowerCamelCase ,			5	)	)	)
		return final[::-1]


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		UpperCamelCase						:				Union[str, Any]             =      [
		    [2, 1, 1, 1, 1, 4],
		    [1, 2, 1, 1, 1, 5],
		    [1, 1, 2, 1, 1, 6],
		    [1, 1, 1, 2, 1, 7],
		    [1, 1, 1, 1, 2, 8],
		]
		print(solve_simultaneous(eq))
		print(solve_simultaneous([[4, 2]]))









"""simple docstring"""


def  __snake_case       (   UpperCamelCase__ ,			UpperCamelCase__ = " "	)      ->		list:







		"""simple docstring"""





		A					       = []

		A					       = 0
		for index, char in enumerate(UpperCamelCase__	):
				if char == separator:
						split_words.append(string[last_index:index]	)
						A					       = index + 1
				elif index + 1 == len(UpperCamelCase__	):
						split_words.append(string[last_index : index + 1]	)
		return split_words


if __name__ == "__main__":
	from doctest import testmod

	testmod()





