Let Cu = 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 row 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 Fu = ke is equivalent to Cu = k and consequently, the cost of an image reconstruction from Fu = ke is reduced.