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The solvent quality determines the collapsed or the expanded state of a polymer. For example, a polymer dissolved in a poor solvent collapses, whereas in a good solvent it opens up. While this standard understanding is generally valid, there are examples when a polymer collapses even in a mixture of two good solvents. This phenomenon, commonly known as co-non-solvency, is usually associated with smart polymers. Moreover, recent experiments have shown that the elastin-like polypeptides (ELPs) show co-non-solvency behavior in aqueous-ethanol mixtures. In this study, we investigate the phase behavior of ELPs in aqueous binary mixtures using molecular dynamics simulations of all-atom and complementary explicit solvent generic models. The model is parameterized by mapping the solvation free energy obtained from the all-atom simulations onto the generic interaction parameters. For this purpose, we derive segment based generic parameters for four different peptides, namely proline (P), valine (V), glycine (G) and alanine (A). Here we compare the conformational behavior of two ELP sequences, namely VPGGG and VPGVG, in aqueous-ethanol and -urea mixtures. Consistent with recent experiments, we find that ELPs show co-non-solvency in aqueous-ethanol mixtures. Ethanol molecules have preferential binding with all ELP residues and thus driving the coil-to-globule transition. On the contrary, ELP conformations show weak variation in aqueous-urea mixtures. Our simulations suggest that the glycine residues dictate the overall behavior of ELPs in aqueous-urea, where urea molecules have a rather weak preferential binding with glycine, i.e., less than kT. While the validation of the latter findings will require more detailed experimental investigation, the results presented here may provide a new twist to the present understanding of cosolvent interactions with peptides and proteins.