Question

Using Solve function in Mathematica, we may get several solutions, e.g.

    In[1]:= Solve[x == 1 &&  2 >= y >= 1, {x, y}, Integers]
    Out[1]= {{x -> 1, y -> 1}, {x -> 1, y -> 2}}

In case there are tens of solutions, the lists above will be messy.
Now I want to list only all possible values of x and y with a list like this

    {x->1, y->1,2}

Is there any easy way to reformat the output of the solution?

Another question, how to use the value from a solution?

    In[1]:= Solve[x == 1,{x}]
    Out[1]= {x -> 1}
    In[2]:= x
    Out[2]= x
    In[3]:= Definition[x]
    Out[3]= Null
    In[4]:= ?x
            Global`x

Answer 1

For your first question you might use:

vars = {x, y};

sols = Solve[x == 1 && 2 >= y >= 1, vars, Integers];

Thread[ vars -> Union /@ (vars /. sols) ]

{x -> {1}, y -> {1, 2}}

---

For your second question please see this answer.

Most handily:

sols = Solve[x^2 + a x + 1 == 0, x]

MapIndexed[(gg[#2[[1]]][a_] := #) &, x /. sols];

This makes assignments to the symbol gg.
The function is then used with the syntax gg[1][17] to mean the first solution, and a == 17:

Plot[gg[1][a], {a, 1, 4}]

gg[2] /@ {1, 2, 3}

{1/2 (-1 + I Sqrt[3]), -1, 1/2 (-3 + Sqrt[5])}