Most attempts for the measurement of line tension in solid-liquid-vapor systems are based on the drop size dependence of contact angles of sessile drops on smooth, homogeneous solid surfaces. Despite being a well-defined thermodynamic quantity, there are still significant discrepancies in both the magnitude and sign of line tension reported in different experimental arrangements and theoretical studies. In order to broaden the scope of experimental studies of line tension, a non-axisymmetric system, i.e., a stripwise heterogeneous wall arrangement, was considered. A numerical scheme has been developed to solve simultaneously both the modified Young equation and the Laplace equation of capillarity for such a stripwise wall and to generate a series of theoretical contact lines for non-zero line tension values. These theoretical curves can be compared to experimental profiles to determine line tension. The preliminary comparison of these curves with an experimental curve suggests that the line tension value is on the order of 10 ร6 (J/m), in agreement with values obtained from drop size dependence of contact angle studies. The comparison also shows that line tension in such systems cannot be as low as 10 ร10 (J/m), i.e., the order of the magnitude obtained from some theoretical studies and experimental approaches.