> S15 := {x+2*y+z = 8, -x+3*y-2*z=1, 3*x + 4*y - 7*z = 10};

  S15 := {x + 2 y + z = 8, -x + 3 y - 2 z = 1, 3 x + 4 y - 7 z = 10}

> read("/afs/eos.ncsu.edu/users/k/kaltofen/www/courses/LinAlgebra/Maple/
> initlib.mpl");

  libname := /afs/eos.ncsu.edu/users/k/kaltofen/www/courses/LinAlg\

        ebra/Maple, "/afs/bp.ncsu.edu/dist/maple551/update",

        "/afs/bp.ncsu.edu/dist/maple551/lib"

> with(refpkg);

       [E_I, E_II, E_III, mydet, myinverse, mysolve, ref, xref]

> infolevel['refpkg']:=3;

                        infolevel[refpkg] := 3

> a := b;

                                a := b

> a;

                                  b

> 'a';

                                  a

> eval('a');

                                  b

> mysolve(S15, {x,y,z});

                                       [ 1    2     1     8]
                                       [                   ]
         Augmented coefficient matrix, [-1    3    -2     1]
                                       [                   ]
                                       [ 3    4    -7    10]

refpkg[ref]   NoName

                          Searching column 1

refpkg[ref]   NoName

                   Added row 1 times , 1,  to row 2

refpkg[ref]   NoName

                         [1    2     1     8]
                         [                  ]
                         [0    5    -1     9]
                         [                  ]
                         [3    4    -7    10]

refpkg[ref]   NoName

                  Added row 1 times , -3,  to row 3

refpkg[ref]   NoName

                       [1     2      1      8]
                       [                     ]
                       [0     5     -1      9]
                       [                     ]
                       [0    -2    -10    -14]

refpkg[ref]   NoName

                          Searching column 2

refpkg[ref]   NoName

                  Added row 2 times , 2/5,  to row 3

refpkg[ref]   NoName

                      [1    2      1        8  ]
                      [                        ]
                      [0    5     -1        9  ]
                      [                        ]
                      [0    0    -52/5    -52/5]


                                [1    2      1        8  ]
                                [                        ]
           REF of coeff mat = , [0    5     -1        9  ]
                                [                        ]
                                [0    0    -52/5    -52/5]


                   Solving for , z,  = , 1,  = , 1


              Solving for , y,  = , 9/5 + 1/5 z,  = , 2


              Solving for , x,  = , 8 - 2 y - z,  = , 3


                        {z = 1, y = 2, x = 3}

> mysolve(S15, {x,y});

                                       [ 1    2     -z + 8 ]
                                       [                   ]
         Augmented coefficient matrix, [-1    3    2 z + 1 ]
                                       [                   ]
                                       [ 3    4    7 z + 10]

refpkg[ref]   NoName

                          Searching column 1

refpkg[ref]   NoName

                   Added row 1 times , 1,  to row 2

refpkg[ref]   NoName

                         [1    2     -z + 8 ]
                         [                  ]
                         [0    5     9 + z  ]
                         [                  ]
                         [3    4    7 z + 10]

refpkg[ref]   NoName

                  Added row 1 times , -3,  to row 3

refpkg[ref]   NoName

                        [1     2     -z + 8  ]
                        [                    ]
                        [0     5      9 + z  ]
                        [                    ]
                        [0    -2    10 z - 14]

refpkg[ref]   NoName

                          Searching column 2

refpkg[ref]   NoName

                  Added row 2 times , 2/5,  to row 3

refpkg[ref]   NoName

                      [1    2        -z + 8    ]
                      [                        ]
                      [0    5        9 + z     ]
                      [                        ]
                      [0    0    -52/5 + 52/5 z]


                                [1    2        -z + 8    ]
                                [                        ]
           REF of coeff mat = , [0    5        9 + z     ]
                                [                        ]
                                [0    0    -52/5 + 52/5 z]


                    Found inconsistency in row , 3


                                  {}

> mysolve({x+y=3, 2*x+2*y=6}, {x,y});

                                           [1    1    3]
             Augmented coefficient matrix, [           ]
                                           [2    2    6]

refpkg[ref]   NoName

                          Searching column 1

refpkg[ref]   NoName

                  Added row 1 times , -2,  to row 2

refpkg[ref]   NoName

                            [1    1    3]
                            [           ]
                            [0    0    0]


                                       [1    1    3]
                  REF of coeff mat = , [           ]
                                       [0    0    0]


                         Free variable(s) , y


               Solving for , x,  = , 3 - y,  = , 3 - y


                          {y = y, x = 3 - y}

> mysolve({x+y=3, 2*x+2*y=6}, {x});

                                          [1     3 - y  ]
            Augmented coefficient matrix, [             ]
                                          [2    -2 y + 6]

refpkg[ref]   NoName

                          Searching column 1

refpkg[ref]   NoName

                  Added row 1 times , -2,  to row 2

refpkg[ref]   NoName

                             [1    3 - y]
                             [          ]
                             [0      0  ]


                                       [1    3 - y]
                  REF of coeff mat = , [          ]
                                       [0      0  ]


               Solving for , x,  = , 3 - y,  = , 3 - y


                             {x = 3 - y}

> mysolve({x + a*y = b, 2*x + 3*y=c}, {x,y});

                                           [2    3    c]
             Augmented coefficient matrix, [           ]
                                           [1    b    b]

refpkg[ref]   NoName

                          Searching column 1

refpkg[ref]   NoName

                 Added row 1 times , -1/2,  to row 2

refpkg[ref]   NoName

                    [2       3             c     ]
                    [                            ]
                    [0    -3/2 + b    - 1/2 c + b]


                              [2       3             c     ]
         REF of coeff mat = , [                            ]
                              [0    -3/2 + b    - 1/2 c + b]


                        - 1/2 c + b                c          b
  Solving for , y,  = , -----------,  = , - 1/2 -------- + --------
                         -3/2 + b               -3/2 + b   -3/2 + b


  Solving for , x,  = , 1/2 c - 3/2 y,  = ,

                       c              b
        1/2 c + 3/4 -------- - 3/2 --------
                    -3/2 + b       -3/2 + b


                c          b
  {y = - 1/2 -------- + --------,
             -3/2 + b   -3/2 + b

                           c              b
        x = 1/2 c + 3/4 -------- - 3/2 --------}
                        -3/2 + b       -3/2 + b

>