The general problem of the one-dimensional linearized simultaneous equations of thermoelasticity has been solved in the Laplace transform domain by following the algebraic eigenvalue approach. This is an alternative which retains the original structure of the problem compared to the recent state space methodology of Bahar and Hetnarski [1, 2]. The use of thermoelastic potential is thus avoided. The results obtained can be used to a broad class of problems in thermoelasticity or other coupled fields. Applications to problems pertaining to a half space and a layer are presented.