Among the existing elemental characterization techniques, particle-induced x-ray emission (PIXE) and energy-dispersive x-ray (EDX) spectroscopy are two of the most widely used in different scientific and technological fields. Here, we present the first quantitative laser-driven PIXE and laser-driven EDX experimental investigation performed at the Centro de Láseres Pulsados in Salamanca. Thanks to their potential for compactness and portability, laser-driven particle sources are very appealing for materials science applications, especially for materials analysis techniques. We demonstrate the possibility to exploit the x-ray signal produced by the co-irradiation with both electrons and protons to identify the elements in the sample. We show that, using the proton beam only, we can successfully obtain quantitative information about the sample structure through laser-driven PIXE analysis. These results pave the way toward the development of a compact and multifunctional apparatus for the elemental analysis of materials based on a laser-driven particle source.