A bimodal optical computer (BOC) for solving a system of linear equations is presented. The BOC can achieve accuracies comparable to those of the digital computer, and its speed is far superior in solving a system of linear equations. The advantage in speed increases with the size of the matrix. The problem of the convergence of the solution using the BOC is investigated. It is found that by using a BOC with an error as high as 50% in the matrix's optical mask and 1% in the electro-optical devices, convergence is achieved for matrices with condition numbers of 25. The effect of the condition number on the convergence of the solution is investigated. It is found that matrices with large condition numbers converge very slowly. Convergence for matrices with condition numbers higher than 250 was achieved. A means of improving the condition number of a matrix is also introduced.