Actual Mathomatic output from the linear script

Mathomatic version 15.1.4 (www.mathomatic.org)
Copyright (C) 1987-2010 George Gesslein II.
100 equation spaces available, 1920 kilobytes per equation space.
HTML color mode enabled; disable with the -c option or "set no color".
1—> ; Combine 3 simultaneous linear equations with 3 unknowns (x, y, z).
1—> ; Solve for all 3 unknowns using the eliminate, solve, and simplify commands.
1—> 
1—> clear all ; restart Mathomatic
1—> ; enter all 3 equations:
1—> d1=a1*x+b1*y+c1*z

#1: d1 = (a1·x) + (b1·y) + (c1·z)

1—> d2=a2*x+b2*y+c2*z

#2: d2 = (a2·x) + (b2·y) + (c2·z)

2—> d3=a3*x+b3*y+c3*z

#3: d3 = (a3·x) + (b3·y) + (c3·z)

3—> 2 ; select equation number 2 as the current equation

#2: d2 = (a2·x) + (b2·y) + (c2·z)

2—> eliminate x ; eliminate variable x from the current equation
Solving equation #1 for (x) and substituting into the current equation...

                  a2·((b1·y) + (c1·z) − d1)
#2: d2 = (b2·y)------------------------- + (c2·z)
                             a1

2—> 3 ; select equation number 3

#3: d3 = (a3·x) + (b3·y) + (c3·z)

3—> eliminate x y ; eliminate variables x and then y from the current equation
Substituting the RHS of equation #1 into the current equation for variable (x)...
Solving equation #2 for (y) and substituting into the current equation...

                                                                b1·((z·((c2·a1)(a2·c1))) + (a2·d1)(d2·a1))
                                                            a3·(------------------------------------------------ + (c1·z) − d1)
         b3·((z·((c2·a1)(a2·c1))) + (a2·d1)(d2·a1))                     ((a2·b1)(b2·a1))
#3: d3 = ------------------------------------------------------------------------------------------------------------------- + (c3·z)
                       ((a2·b1)(b2·a1))                                                  a1

3—> z ; solve and find z

        ((d3·((a2·b1)(a1·b2))) + (b3·((d2·a1)(a2·d1))) + (a3·((b2·d1)(b1·d2))))
#3: z = --------------------------------------------------------------------------------
        ((b3·((c2·a1)(a2·c1))) + (a3·((b2·c1)(b1·c2))) + (c3·((a2·b1)(a1·b2))))

3—> 2 ; select equation number 2

        ((z·((c2·a1)(a2·c1))) + (a2·d1)(d2·a1))
#2: y = ---------------------------------------------
                     ((a2·b1)(b2·a1))

2—> eliminate z using 3 ; find y by combining equation numbers 2 and 3
Substituting the RHS of equation #3 into the current equation for variable (z)...

         ((d3·((a2·b1)(a1·b2))) + (b3·((d2·a1)(a2·d1))) + (a3·((b2·d1)(b1·d2))))·((c2·a1)(a2·c1))
        (---------------------------------------------------------------------------------------------------- + (a2·d1)(d2·a1))
                   ((b3·((c2·a1)(a2·c1))) + (a3·((b2·c1)(b1·c2))) + (c3·((a2·b1)(a1·b2))))
#2: y = --------------------------------------------------------------------------------------------------------------------------
                                                           ((a2·b1)(b2·a1))

2—> simplify

        ((a1·((d3·c2)(d2·c3))) + (d1·((a2·c3)(c2·a3))) + (c1·((d2·a3)(d3·a2))))
#2: y = --------------------------------------------------------------------------------
        ((a1·((b3·c2)(c3·b2))) + (c1·((a3·b2)(b3·a2))) + (b1·((c3·a2)(a3·c2))))

2—> 1 ; select equation number 1

        -((b1·y) + (c1·z) − d1)
#1: x = -----------------------
                  a1

1—> eliminate z using 3 y using 2; find x
Substituting the RHS of equation #3 into the current equation for variable (z)...
Substituting the RHS of equation #2 into the current equation for variable (y)...

          b1·((a1·((d3·c2)(d2·c3))) + (d1·((a2·c3)(c2·a3))) + (c1·((d2·a3)(d3·a2))))   c1·((d3·((a2·b1)(a1·b2))) + (b3·((d2·a1)(a2·d1))) + (a3·((b2·d1)(b1·d2))))
        -(----------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------- − d1)
           ((a1·((b3·c2)(c3·b2))) + (c1·((a3·b2)(b3·a2))) + (b1·((c3·a2)(a3·c2))))      ((b3·((c2·a1)(a2·c1))) + (a3·((b2·c1)(b1·c2))) + (c3·((a2·b1)(a1·b2))))
#1: x = ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                               a1

1—> 
1—> simplify all ; simplify and list all solutions

        ((c1·((b2·d3)(b3·d2))) + (b1·((c3·d2)(c2·d3))) + (d1·((b3·c2)(c3·b2))))
#1: x = --------------------------------------------------------------------------------
        ((a1·((b3·c2)(c3·b2))) + (c1·((a3·b2)(b3·a2))) + (b1·((c3·a2)(a3·c2))))


        ((a1·((d3·c2)(d2·c3))) + (d1·((a2·c3)(c2·a3))) + (c1·((d2·a3)(d3·a2))))
#2: y = --------------------------------------------------------------------------------
        ((a1·((b3·c2)(c3·b2))) + (c1·((a3·b2)(b3·a2))) + (b1·((c3·a2)(a3·c2))))


        ((b1·((d3·a2)(a3·d2))) + (a1·((b3·d2)(d3·b2))) + (d1·((a3·b2)(b3·a2))))
#3: z = --------------------------------------------------------------------------------
        ((a1·((b3·c2)(c3·b2))) + (c1·((a3·b2)(b3·a2))) + (b1·((c3·a2)(a3·c2))))

Finished reading file "linear.in".
1—> 
End of input.


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