We present the Sunyaev-Zel'dovich (SZ) effect observations of a sample of 25 massive relaxed galaxy clusters observed with the Sunyaev-Zel'dovich array (SZA), an eight-element interferometer that is part of the Combined Array for Research in Millimeter-wave Astronomy (CARMA). We performed an analysis of new SZA data and archival Chandra observations of this sample to investigate the integrated pressure-a proxy for cluster mass-determined from x-ray and SZ observations, two independent probes of the intra-cluster medium (ICM). This analysis makes use of a model for the ICM introduced by Bulbul (2010 Astrophys. J. 720 1038) which can be applied simultaneously to the SZ and x-ray data. With this model, we estimated the pressure profile for each cluster using a joint analysis of the SZ and x-ray data, and using the SZ data alone. We found that the integrated pressures measured from the x-ray and SZ data are consistent. This conclusion is in agreement with recent results obtained using WMAP and Planck data, confirming that SZ and x-ray observations of massive clusters detect the same amount of thermal pressure from the ICM. To test for possible biases introduced by our choice of model, we also fitted the SZ data using the universal pressure profile proposed by Arnaud (2010 Astron. Astrophys. 517 A92) and found consistency between the two models out to r500 in the pressure profiles and integrated pressures.