Scattering amplitudes for coupled πΛ, πΣ, and K̄N channels are obtained by an extension of the method of Amati, Stanghellini, and Vitale. The method is shown to be essentially equivalent to the ND method in the region of nonrelativistic baryon energies, under the assumption that the only important forces arise from the Born singularities. All possibilities for the ΣΛ and K̄Λ relative parities are considered. The aim is to see to what extent earlier calculations, which neglect the K̄-N interactions, are modified by its inclusion. If the K̄N coupling constants are as strong as the πN coupling, significant quantitative and qualitative modifications are obtained: an I=1, J=32 resonance with the properties of the Y1* may be obtained for P(ΣΛ)=+/-1 an I=0 resonance with the location and width of the Y0* may be obtained for P(ΣΛ)=-1, in the P12 state, and for P(ΣΛ)=+1, in the P32 state. If the K̄N couplings are significantly weaker than the πN coupling, a P32 resonance with the properties of the Y1* is obtained only if P(ΣΛ)=+1 and if the ΣΣπ coupling is very weak; in this case one obtains no I=0 resonance identifiable with the Y0*. An I=0, P32 resonance at 1520 MeV may be obtained with a wide variety of couplings for P(ΣΛ)=+1 the predicted width of this resonance is very large (Γ2>50 MeV). Resonances in other states, multichannel effects on resonance shapes, and KN elastic scattering are discussed.