





"""simple docstring"""
def 					__lowerCamelCase       (							a_					:		list[int]			,       a_					:		list[int]							)      ->				tuple[float, float]:

      # Check if the input is valid
      if not len(a_							) == len(a_							) == 3:
            raise ValueError('''Please enter a valid equation.'''							)
      if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
            raise ValueError('''Both a & b of two equations can\'t be zero.'''							)

      # Extract the coefficients
      __SCREAMING_SNAKE_CASE    ,__SCREAMING_SNAKE_CASE    ,__SCREAMING_SNAKE_CASE       :int		    =  equationa
      __SCREAMING_SNAKE_CASE    ,__SCREAMING_SNAKE_CASE    ,__SCREAMING_SNAKE_CASE       :Optional[Any]		    =  equationa

      # Calculate the determinants of the matrices
      __SCREAMING_SNAKE_CASE       :Any		    =  aa * ba - aa * ba
      __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  ca * ba - ca * ba
      __SCREAMING_SNAKE_CASE       :Any		    =  aa * ca - aa * ca

      # Check if the system of linear equations has a solution (using Cramer's rule)
      if determinant == 0:
            if determinant_x == determinant_y == 0:
                  raise ValueError('''Infinite solutions. (Consistent system)'''							)
            else:
                  raise ValueError('''No solution. (Inconsistent system)'''							)
      else:
            if determinant_x == determinant_y == 0:
                  # Trivial solution (Inconsistent system)
                  return (0.0, 0.0)
            else:
                  __SCREAMING_SNAKE_CASE       :str		    =  determinant_x / determinant
                  __SCREAMING_SNAKE_CASE       :Dict		    =  determinant_y / determinant
                  # Non-Trivial Solution (Consistent system)
                  return (x, y)






"""simple docstring"""
import math
import unittest



def 					__lowerCamelCase       (							a_					:		int							)      ->				bool:
      assert isinstance(a_			,       a_							) and (
          number >= 0
      ), "'number' must been an int and positive"

      if 1 < number < 4:
            # 2 and 3 are primes
            return True
      elif number < 2 or number % 2 == 0 or number % 3 == 0:
            # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
            return False

      # All primes number are in format of 6k +/- 1
      for i in range(5			,       int(math.sqrt(a_							) + 1							)			,       6							):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True






class  _SCREAMING_SNAKE_CASE(       unittest.TestCase  ):




       def    _UpperCamelCase					(						self							)      ->				Union[str, Any]:





             """simple docstring"""






             self.assertTrue(is_prime(2							)							)
             self.assertTrue(is_prime(3							)							)
             self.assertTrue(is_prime(5							)							)
             self.assertTrue(is_prime(7							)							)
             self.assertTrue(is_prime(11							)							)
             self.assertTrue(is_prime(13							)							)
             self.assertTrue(is_prime(17							)							)
             self.assertTrue(is_prime(19							)							)
             self.assertTrue(is_prime(23							)							)
             self.assertTrue(is_prime(29							)							)




       def    _UpperCamelCase					(						self							)      ->				Tuple:





             """simple docstring"""






             with self.assertRaises(SCREAMING_SNAKE_CASE__							):
                   is_prime(-19							)
             self.assertFalse(
                 is_prime(0							)		,'''Zero doesn\'t have any positive factors, primes must have exactly two.'''		,)
             self.assertFalse(
                 is_prime(1							)		,'''One only has 1 positive factor, primes must have exactly two.'''		,)
             self.assertFalse(is_prime(2 * 2							)							)
             self.assertFalse(is_prime(2 * 3							)							)
             self.assertFalse(is_prime(3 * 3							)							)
             self.assertFalse(is_prime(3 * 5							)							)
             self.assertFalse(is_prime(3 * 5 * 7							)							)


if __name__ == "__main__":
  unittest.main()