### Method for solving a large system of under-determined equations?

I am trying to parametrize and find a family of solutions to some equations. (I am using the `solve([eqns],vars)`

function.) Unfortunately, the equations are just complicated enough so that rather than parametrize, sage gives up and outputs the equations themselves.

Here is a (partial) particular example that I had in mind. My real equation is actually a bit more complicated. But this is a point where it went from solving to simply spitting out the original equations. Here is the output:

```
10 equations, and 12 unknowns.
{s0 + s2 + s4: 1}
{s5: 0}
{s0 + s1 + s2 + s3 + s4 + s5: 2}
{w0: s5}
{w1: -s4}
{w2: s3}
{(s0*w0 + s1*w1)*(s0*w0 + s1*w1 + s2*w2): s2*w0 + s3*w1}
{w3: -s2}
{w4: s1}
{w5: -s0}
```

Is there anything I can do? I've read the solve and x.solve pages, but I don't see a clear method I should ~~try... ~~try...

===========

Edit: I'm looking for the simplest representation of this system of equations. I would like Sage to parametrize a few of the variables and solve for the others.
For instance, a linear system example would be the following:

`eq1=a+b+c==2`

`eq2=b==1`

`solve([eq1,eq2],a,b,c)`

The output would be:

`a=1-r1, b=1, c=r1`

Sage can do this using the `solve`

function for small simple situations, even if they're non-linear equations. I want it to classify the family of all possible (real) solutions which satisfy all of the equations simultaneously. But it's stopping when I have a complicated system of equations.