Question

Ayuda con procedimiento y respuesta

Answer 1

Se trata de un sistema de ecuaciones 2x2

Introduciendo cambio de variable
         1/x = m       1/y = n

Con este cambio, las ecuaciones quedan

              m + n = 2a/[(a + b)(a - b)]        (1)

           3m - 2n = (a - 5b)/(a^2 - b^2)
           3m - 2n = (a - 5b)/[(a + b)(a - b)]      (2)

Resolviendo sistema (1) (2)
   (1) x 2
                 2m + 2n = 4a[(a + b)(a - b)]      (3)
   (2) + (3)
                          5m = [(a - 5b) + 4a]/[(a + b)(a - b)]

                                = (5a - 5b)/[(a + b)(a - b)]

                          5m = 5(a - b)/[(a + b)(a - b)]
                                                                         m = 1/(a + b)
    m en (1)
                       1/(a + b) + n = 2a/[(a + b)(a - b)]

                                        n = 2a/[(a + b)(a - b)] - 1/(a + b)

                                           = [(2a - 1)/[(a + b)(a - b)]

                                           = [2a - (a - b)]/([(a + b)(a - b)]

                                           = (2a - a + b)/[(a + b)(a - b)]

                                           = (a + b)/[(a + b)(a - b)]
                                                                                   n = 1/(a - b)
Volviedo a las variables originales
                            m = 1/x
                            x = 1/m
                            x = 1/[1/(a + b)]
                                                              x = a + b
                           n = 1/y
                           y = 1/n
                           y = 1/[1/(a - b)]
                                                              y = a - b

                                                                          S = {(a + b), (a - b)}