Researchers have developed a fast and reliable method to solve complex linear systems with uncertainties in both the coefficients and the results. This method, called weighted total least squares, can handle correlations between the coefficients and results, making it useful in various fields like metrology and geodesy. The approach presented in the study allows for the efficient computation of solutions and their covariance matrices. By testing the method on different cases, the researchers confirmed its accuracy and effectiveness. Additionally, the method can easily accommodate error-free coefficients, simplifying the process further. The code for implementing this method in MATLAB is also provided for practical use.