This paper presents computer simulations of CuxZr100−x(x=36,50,64) in the liquid and glass phases. The simulations are based on the effective-medium theory potentials. We find good invariance of both structure and dynamics in reduced units along the isomorphs of the systems. The state points studied involve a density variation of almost a factor of 2 and temperatures going from 1500 K to above 4000 K for the liquids and from 500 K to above 1500 K for the glasses. For comparison, results are presented also for similar temperature variations along isochores, showing little invariance. In general for a binary system the phase diagram has three axes: composition, temperature, and pressure (or density). When isomorphs are present, there are effectively only two axes, and for a fixed composition there is just one. We conclude that the liquid and glass parts of the thermodynamic phase diagram of this metallic glass former at a fixed composition are effectively one-dimensional in the sense that many physical properties are invariant along the same curves, implying that in order to investigate the phase diagram, it is only necessary to go across these curves.