Cloud-point and bubble-point data to $170^{circ}C$ and 50 bar are presented for four different solvents, normal pentane. n-hexane, n-heptane, and n-octane with poly(ethylene-co-42 wt% octene) ($PEO_{42}$) copolymer. The pressure-concentration isotherms measured for $PEO_{42}$ - normal pentane have maximums at around 5 wt% of the copolymer concentrations in the solution. $PEO_{42}$- normal pentane system exhibits LCST-type phase behavior at temperatures greater than $130^{circ}C$. Below $120^{circ}C$, bubble-point type transitions are observed. However, the binary mixtures for $PEO_{42}$ in n-hexane, n-heptane, and n-octane have only bubble-point type transitions at the pressure-temperature region investigated in this study. The single-phase region of PEO - alkane mixtures increases with the molecular size of alkane solvent due to the increasing dispersion interactions between PEO and the alkane.