Mathomatic version 14.0.4 (www.mathomatic.org)
Copyright (C) 1987-2008 George Gesslein II.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

100 equation spaces available, 960 kilobytes per equation space.
HTML color mode enabled.
1—> ; Combine 3 simultaneous linear equations with 3 unknowns (x, y, z).
1—> ; Solve for all 3 unknowns using the "eliminate" command.
1—> 
1—> clear all
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

#2: d2 = (a2·x) + (b2·y) + (c2·z)

2—> eliminate x
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
Solving equation #1 for (x) and substituting into the current equation...
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—> solve verify z ; solve for z, verifying the result

        ((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))))

Division simplified with polynomial GCD.
Division simplified with polynomial GCD.
Division simplified with polynomial GCD.
Solution verified.
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
Solving equation #3 for (z) and substituting into the current equation...

         ((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—> 1 ; select equation number 1

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

1—> eliminate y z
Solving equation #2 for (y) and substituting into the current equation...
Solving equation #3 for (z) and substituting into the current equation...

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

1—> simplify all ; list all solutions

        ((b1·((c3·d2) − (c2·d3))) + (c1·((d3·b2) − (b3·d2))) + (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) − (c3·d2))) + (c1·((a3·d2) − (d3·a2))) + (d1·((c3·a2) − (a3·c2))))
#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.