
"""simple docstring"""





def 				lowerCamelCase__		(      __snake_case,					__snake_case     )							->		tuple[float, float]:


					"""simple docstring"""





					if not len(__snake_case     ) == len(__snake_case     ) == 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
					_UpperCamelCase			,  _UpperCamelCase			,  _UpperCamelCase										=  equationa
					_UpperCamelCase			,  _UpperCamelCase			,  _UpperCamelCase										=  equationa

					# Calculate the determinants of the matrices
					_UpperCamelCase										=  aa * ba - aa * ba
					_UpperCamelCase										=  ca * ba - ca * ba
					_UpperCamelCase										=  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:
															_UpperCamelCase										=  determinant_x / determinant
															_UpperCamelCase										=  determinant_y / determinant
															# Non-Trivial Solution (Consistent system)
															return (x, y)








"""simple docstring"""





def 				lowerCamelCase__		(      __snake_case,					__snake_case     )							->		str:


					"""simple docstring"""





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

					_UpperCamelCase										=  str(bin(__snake_case     )     )
					binary_number += "0" * shift_amount
					return binary_number



def 				lowerCamelCase__		(      __snake_case,					__snake_case     )							->		str:


					"""simple docstring"""





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

					_UpperCamelCase										=  str(bin(__snake_case     )     )[2:]
					if shift_amount >= len(__snake_case     ):
										return "0b0"
					_UpperCamelCase										=  binary_number[: len(__snake_case     ) - shift_amount]
					return "0b" + shifted_binary_number



def 				lowerCamelCase__		(      __snake_case,					__snake_case     )							->		str:


					"""simple docstring"""





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

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


if __name__ == "__main__":
				import doctest

				doctest.testmod()






