This work proposes a method for assessing the detective quantum efficiency (DQE) of radiographic imaging systems that include both the x-ray detector and the antiscatter device. Cascaded linear analysis of the antiscatter device efficiency (DQEASD) with the x-ray detector DQE is used to develop a metric of system efficiency (DQEsys); the new metric is then related to the existing system efficiency parameters of effective DQE (eDQE) and generalized DQE (gDQE). The effect of scatter on signal transfer was modelled through its point spread function (PSF), leading to an x-ray beam transfer function (BTF) that multiplies with the classical presampling modulation transfer function (MTF) to give the system MTF. Expressions are then derived for the influence of scattered radiation on signal-difference to noise ratio (SDNR) and contrast-detail (c-d) detectability. The DQEsys metric was tested using two digital mammography systems, for eight x-ray beams (four with and four without scatter), matched in terms of effective energy. The model was validated through measurements of contrast, SDNR and MTF for poly(methyl)methacrylate thicknesses covering the range of scatter fractions expected in mammography. The metric also successfully predicted changes in c-d detectability for different scatter conditions. Scatter fractions for the four beams with scatter were established with the beam stop method using an extrapolation function derived from the scatter PSF, and validated through Monte Carlo (MC) simulations. Low-frequency drop of the MTF from scatter was compared to both theory and MC calculations. DQEsys successfully quantified the influence of the grid on SDNR and accurately gave the break-even object thickness at which system efficiency was improved by the grid. The DQEsys metric is proposed as an extension of current detector characterization methods to include a performance evaluation in the presence of scattered radiation, with an antiscatter device in place.