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Here is a procedure (not tested enough).
The system must be polynomial with rational coefficients.

solpart:=proc(sys::list(relation))
local i,r1,r2,rez:=NULL, sd:=SolveTools:-SemiAlgebraic(sys);
#print(sd);
if sd=[] then return [] else sd:=sd[1] fi;
for i to nops(sd) do
   r1:=eval(sd[i],[rez]); 
   if type(r1,`=`) then rez:=rez,r1; next; fi;
   if i=nops(sd) then
     if     type(rhs(r1),realcons) then rez:=rez,lhs(r1)=rhs(r1)-1
     elif   type(lhs(r1),realcons) then rez:=rez,rhs(r1)=lhs(r1)+1
     else error "Strange1"; fi;
   return rez;
   fi; 
   
   r2:=eval(sd[i+1],[rez]);   #print([r1,r2]);
   if    type(rhs(r1),name) and (rhs(r1)=lhs(r2)) then i:=i+1; rez:=rez, rhs(r1)=eval((lhs(r1)+rhs(r2))/2,[rez]) 
   elif  type(lhs(r1),name) and (lhs(r1)=rhs(r2)) then i:=i+1; rez:=rez, lhs(r1)=eval((rhs(r1)+lhs(r2))/2,[rez])
   elif  type(rhs(r1),realcons) then rez:=rez,lhs(r1)=rhs(r1)-1
   elif  type(lhs(r1),realcons) then rez:=rez,rhs(r1)=lhs(r1)+1
   else error "Strange2"; fi;
od;
rez
end:

solpart([x*y-1<=0, x>0, y > 1]);
        y = 2, x = 1/4

solpart([x*y-1<0, x>0, y >= 1]);
        y = 1, x = 1/2

f:=proc(n::posint,i)
   local k, s:=add(i[k],k=1..n), p:=mul(i[k],k=1..n);
   add(p/i[k]*(s-i[k]), k=1..n)
end:

f(4,i);
      

Int(1/(sqrt(t^4+1)+t^2), t = 1 .. infinity):
% = value(%);
evalf(%); #check

        0.4799537050 = 0.4799537050

Such a system will have generally 2^18 = 262144 solutions.
E.g. the simple one
{seq(x[k]^2=1,k=1..18)};

has exactly 2^18 solutions (all are real). For a more realistic system each solution will be huge.
So, you have no chance. You can at most use fsolve to find some of them.

solve(convert(eq-K,list));

You should use simply  sol(1);

If you really want such a manipulation, use:

eval('''sol'''(x), [x = X]);
eval(%, X=1);

This is not related to Special Relativity.

solve([2*x=6, y=2], x);
has no solutions because y is seen as a parameter. Only when y=2 a solution exists.
You may see this using

solve([2*x=6, y=2], x, parametric);

Of couse the system can be solved wrt all the variables:
solve([2*x=6, y=2], [x,y]);   # or    solve([2*x=6, y=2]);
      [[x = 3, y = 2]]

 

1. Strangely, for name instead of symbol it works.

3. Workaround:

e:=hypergeom([], [], a)+hypergeom([], [], b):
E:=subs(hypergeom=HG,e):
applyrule(HG(x1::anything, x2::anything, a) = 0, E):
subs(HG=hypergeom,%);

Or, use %hypergeom.

You have overlapping patterns, so both

    true, [x = 2]
    true, [y = 2]

are correct.

For uniqueness use e.g.

typematch({2}, set({x :: odd, y :: even}), 's'); s;

Yes, it seems to be a bug. It should give an error as in:
C:=Matrix(B);
A.C;

You should check whether it is fixed in the development library; see:
https://www.mapleprimes.com/questions/222498-Issues-With-Pdsolve