





def 		_SCREAMING_SNAKE_CASE     ( lowerCAmelCase__							,lowerCAmelCase__						):

		# Check if the input is valid
		if not len(lowerCAmelCase__						) == len(lowerCAmelCase__						) == 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
		lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_	:     int 						=      equationa
		lowerCamelCase_						,      lowerCamelCase_						,      lowerCamelCase_	:     Optional[int] 						=      equationa

		# Calculate the determinants of the matrices
		lowerCamelCase_	:     Tuple 						=      aa * ba - aa * ba
		lowerCamelCase_	:     int 						=      ca * ba - ca * ba
		lowerCamelCase_	:     Optional[int] 						=      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:
						lowerCamelCase_	:     List[Any] 						=      determinant_x / determinant
						lowerCamelCase_	:     Tuple 						=      determinant_y / determinant
						# Non-Trivial Solution (Consistent system)
						return (x, y)







def 		_SCREAMING_SNAKE_CASE     ( lowerCAmelCase__							,lowerCAmelCase__						):
		if number < 0 or shift_amount < 0:
				raise ValueError('both inputs must be positive integers'						)

		lowerCamelCase_	:     int 						=      str(bin(lowerCAmelCase__						)						)
		binary_number += "0" * shift_amount
		return binary_number


def 		_SCREAMING_SNAKE_CASE     ( lowerCAmelCase__							,lowerCAmelCase__						):
		if number < 0 or shift_amount < 0:
				raise ValueError('both inputs must be positive integers'						)

		lowerCamelCase_	:     Union[str, Any] 						=      str(bin(lowerCAmelCase__						)						)[2:]
		if shift_amount >= len(lowerCAmelCase__						):
				return "0b0"
		lowerCamelCase_	:     List[str] 						=      binary_number[: len(lowerCAmelCase__						) - shift_amount]
		return "0b" + shifted_binary_number


def 		_SCREAMING_SNAKE_CASE     ( lowerCAmelCase__							,lowerCAmelCase__						):
		if number >= 0:  # Get binary representation of positive number
				lowerCamelCase_	:     List[Any] 						=      '0' + str(bin(lowerCAmelCase__						)						).strip('-'						)[2:]
		else:  # Get binary (2's complement) representation of negative number
				lowerCamelCase_	:     Any 						=      len(bin(lowerCAmelCase__						)[3:]						)  # Find 2's complement of number
				lowerCamelCase_	:     List[str] 						=      bin(abs(lowerCAmelCase__						) - (1 << binary_number_length)						)[3:]
				lowerCamelCase_	:     List[str] 						=      (
				    '1' + '0' * (binary_number_length - len(lowerCAmelCase__						)) + binary_number
				)

		if shift_amount >= len(lowerCAmelCase__						):
				return "0b" + binary_number[0] * len(lowerCAmelCase__						)
		return (
		    "0b"
		    + binary_number[0] * shift_amount
		    + binary_number[: len(lowerCAmelCase__						) - shift_amount]
		)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
