For a overdetermined linear system of equations Ax=b where A is a full rank matrix with m rows and n columns, b is a vector with m components, b is not in the range of A. The proposal of this work is to extract n+1 linear independent rows of the augmented matrix [A b] using a simulated LU factorization. Then apply the LSQR method to the resulting n+1 equation. When applying the LSQR method to the reduced system the same solution is obtained than the original system but in less time and iteration number.