Question

Resolva os sistemas:

a) y = x + 2
y + x = 14 - x

b) 4 ( x + y/6 =18
2x - y = 13

c) 12x - 5y = 18
y - 2/3 x = -1

OBS : Só respostas.

Answer 1

a)
            y = x + 2  
                   y - x = 2         (1)
            y + x = 14 - x 
                  y + 2x = 14        (2)

      Resolvendo
       (1) x 2
                  2y - 2x = 4      (1a)
       (2) + (1a)
                        3y = 18
                          y = 18/3
                                              y = 6
      y em (1)
                        6 - x = 2
                        6 - 2 = x
                                               x = 4
                                                                   SOLUÇÃO SISTEMA
                                                                            x = 4
                                                                            y = 6

b)
     Igual anterior
         4( x + y/6 =18
   efetuando
         4x + 4y = 6.18
                             4x + 4y = 108        (1)
                             2x - y = 13             (2)
   (2) x 4
                             8x - 4y = 52           (2a)
    (1) + (2a)
                                    12x = 160
                                        x = 160/12
                                                              x = 40/3
         x em (2)
                           2(40/3) - 4y = 52
                           80/3 - 52 = 4y
                           80/3 - 156/3 = 4y
                                     - 76/3 = 4y
                                             y = - 76/(3.4)
                                                = - 76/12
                                                                     y = - 19/3
                                    SOLUÇÃO SISTEMA
                                                x = 40/3
                                                y = - 19/3
c)
           12x - 5y = 18        (1)
           y - 2/3 x = -1         (2)
 (2)x 5
         5y - [(10)/3]x = - 5   (2a)
 (1) + (2a)
                       12x + (10/3)x = 13
                       (36/3)x + (10/3)x = 13
                                      (46/3)x = 13
                                            46x = 39
                                                                  x = 39/46
      x em (1)
                       12(39/46) - 5y = 18
                       (6.39)/23 - 18 = 5y
                          243/23 - 414/23 = 5y
                                        171/23 = 5y
                                          y = - 171/(23.5)
                                                                y = - 171/115
         SOLUÇÃO SISTEMA
                 x = 39/46
                 y = - 171/115