Let C u = k be an underdetermined linear system generated by the strip-based projection model in discrete tomography, where C is row-rank deficient. In the case of one scanning direction the linear dependency of the rows of C is studied in this paper. An index set H is specified such that if all rows of C with row indices in H are deleted then the rows of resultant matrix F are maximum linearly independent rows of C . Therefore, the corresponding system F u= k is equivalent to C u = k and consequently, the cost of an image reconstruction from F u= k is reduced.