; Combine 3 simultaneous linear equations with 3 unknowns (x, y, z).
; Solve for all 3 unknowns using the eliminate, solve, and simplify commands.

clear all ; restart Mathomatic
; enter all 3 equations:
d1=a1*x+b1*y+c1*z
d2=a2*x+b2*y+c2*z
d3=a3*x+b3*y+c3*z
2 ; select equation number 2 as the current equation
eliminate x ; eliminate variable x from the current equation
3 ; select equation number 3
eliminate x y ; eliminate variables x and then y from the current equation
z ; solve and find z
2 ; select equation number 2
eliminate z using 3 ; find y by combining equation numbers 2 and 3
simplify
1 ; select equation number 1
eliminate z using 3 y using 2; find x

simplify all ; simplify and list all solutions