Solution of "borderline" eqs. in Mathematica, Maple, and Maxima (was "linsolve")

To shed some light on the "linsolve, etc" discussion, I did the 
following experiments in solving simple "borderline" equations with 
Mathematica, Maple, and Maxima.

Mathematica 5
==============

Solve[{x==2,y==3}, {x}]
{{x -> 2}}

Solve[{x==2,y==3}, {x,y}]
{{x -> 2, y -> 3}}

Solve[{x==a,y==b}, {x}]
{{x -> a}}

Solve[x==a*x, x]
{{x -> 0}}

Solve[x==a*x, {a,x}]
Solve::svars: Equations may not give solutions for all "solve" variables.
{{a -> 1}, {x -> 0}}

Solve[x/x==1, x]
{{}}

Solve[{x==2,y==x+3,y==1}, {x,y}]
{}

Solve[{x==2,y==x+3,y==1}, x]
{}

Solve[{x==2,y==3,y==1}, x]
{}


Maple 10
========

solve([x=2,y=3], [x]); 

[]

solve([x=2,y=3], [x,y]);
[[x = 2, y = 3]]

solve([x=a,y=b],[x]);
[]

solve(x=a*x,x);
0

solve(x=a*x, [x,a]);
[[x = 0, a = a], [x = x, a = 1]]

solve(x/x=1,x);
x

solve(x/x=1,[x]);
[[x = x]]

solve([x=2,y=x+3,y=1], [x,y]);
[]

solve([x=2,y=x+3,y=1], [x]);
[]

solve([x=2,y=x+3,y=1], [x]);
[]

solve([x=2,y=3,y=1], [x]);
[]


Maxima 5.11
============

solve([x=2,y=3], [x]);
Lisp error

solve([x=a,y=b],[x]);
Lisp error

solve([x=2,y=3], [x,y]);
[[x = 2, y = 3]]

solve(x=a*x,x);
[x=0]

solve(x=a*x, [x,a]);
[[x = 0, a = %r1], [x = %r2, a = 1]]

solve(x/x=1,x);
all

solve([x=2,y=x+3,y=1], [x,y]);
Lisp error

solve([x=2,y=x+3,y=1], [x]);
Lisp error

solve([x=2,y=x+3,y=1], [x]);
Lisp error

solve([x=2,y=3,y=1], [x]);
Lisp error

				Kostas