20x + 15y + 12z = 60 ⇒ 20x + 15y + 12z = 60
10x + 30y + 12z = 60 ⇒ 20x + 60y + 24z = 120
                         -45y - 12z = -60
                   -45y + 45y - 12z = -60 + 45y
                             -12z = -60 + 45y
                              -12      -12
                                z = 5 - 45/12y
            20x + 15y + 12(5 - 45/12y) = 60
         20x + 15y + 12(5) - 12(45/12y) = 60
                20x + 15y + 60 - 45y = 60
                20x + 15y - 45y + 60 = 60
                     20x - 30y + 60 = 60
                              -60  -60
                         20x - 30y = 0
                     20x - 20x - 30y = 0 - 20x
                              -30y = -20x
                              -30   -30
                                y = 2x/3
        20x + 15(2x/3) + 12(5 - 45/12y) = 60
                20x + 10x + 60 - 45y = 60
                     30x - 45y + 60 = 60
                              -60 -60
                         30x - 45y = 0
                    30x - 45y + 45y = 0 + 45y
                             30x = 45y
                              30   30
                               x = 3/2y
    20(3/2y) + 15(2x/3) + 12(5 - 45/12y) = 60
               30y + 10x + 60 - 45y = 60
                10x + 30y - 45y + 60 = 60
                    10x - 15y + 60 = 60
                              -60 -60
                        10x - 15y = 0
    10(3/2y) + 30(2x/3) + 12(5 - 45/12y) = 60
                15y + 20x + 60 - 45y = 60
                20x + 15y - 45y + 60 = 60   Â
                      20x - 30y + 60 = 60        Â
                              -60 -60
                         20x - 30y = 0
           10x - 15y = 0 ⇒ 20x - 30y = 0
           20x - 30y = 0 ⇒ 20x - 30y = 0
                             -60y = 0
                             -60  -60
                               y = 0
                       10x - 15(0) = 0
                          10x - 0 = 0
                              +0 +0
                             10x = 0
                              10  10
                               x = 0
                   20x + 15y + 12z = 60
                 20(0) + 15(0) + 12z = 60
                       0 + 0 + 12z = 60
                          0 + 12z = 60
                             12z = 60
                             12   12
                               z = 5
                           (x, y, z) = (0, 0, 5)