Differential cross sections and photon-beam asymmetries have been measured for the γ→n→K+Σ- and γ→p→K+Σ0 reactions separately using liquid deuterium and hydrogen targets with incident linearly polarized photon beams of Eγ=1.5-2.4GeV at 0. 6<cos¡ΘcmK<1. The cross section ratio of σK+Σ-/ σK+Σ0, expected to be 2 on the basis of the isospin 1/2 exchange, is found to be close to 1. For the K+Σ- reaction, large positive asymmetries are observed, indicating the dominance of K* exchange. The large difference between the asymmetries for the K+Σ- and K+Σ0 reactions cannot be explained by simple theoretical considerations based on Regge model calculations.