The paper demonstrates that in computing a linear form (g, x) of the solution of a system of linear equations Ax = f, the round-off error depends on the quantities ||A-1!f|| and ||AT-1 g|| rather than on the condition number of the coefficient matrix A. Estimates of the inherent and round-off errors in solving the above problem by the orthogonalization method are provided. Numerical results confirming theoretical conclusions are presented.