Measurements of the ac magnetic susceptibility, magnetization, and electrical resistivity at hydrostatic pressures up to 15 kbar and of the thermal expansion were made for the ${\mathrm{Eu}}_{\mathrm{x}}$${\mathrm{Yb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ alloy system (x\ensuremath{\le}0.4) in temperatures from 1.6 to 400 K. The paramagnetic-ferromagnetic transition temperature ${T}_{c}$ versus pressure p curve for x=0.025 has a maximum near p=1 kbar. For x=0.25, ${T}_{c}$ decreases and the ferromagnetic--spin-glass-like transition temperature ${T}_{t}$ increases at rates of \ensuremath{\Delta}${T}_{c}$/\ensuremath{\Delta}p=-9.5 K/kbar and \ensuremath{\Delta}${T}_{t}$/\ensuremath{\Delta}p=+1.7 K/kbar, respectively. The ferromagnetic region disappears near p=2.5 kbar, and above it the paramagnetic--spin-glass-like transition temperature ${T}_{g}$, which is pressure insensitive, appears. The ${T}_{g}$ value for x=0.35 decreases initially and increases slowly with increasing p above p=2 kbar at a rate of \ensuremath{\Delta}${T}_{g}$/\ensuremath{\Delta}p=+0.15 K/kbar. Both the magnetization in the ferromagnetic concentration range and the value of the ac magnetic susceptibility near ${T}_{g}$ in the spin-glass-like state decrease with increasing p. From electrical-resistivity measurements under various pressures, semiconducting character was observed at the ambient pressure for x=0.35 and the transition from semimetallic to semiconducting states appears with increasing p for x=0.025. Thermal expansion shows the large positive volume magnetostriction. These results of the measurements under pressure are discussed on the basis of the Ruderman-Kittel-Kasuya-Yosida interaction by considering that the dominant variable is the number of carriers (electrons or holes) which is strongly controlled by the pressure.