From a matrix `m={{1, 1}, {-1, 1}}`, a vector `b={1, 2}`, and a list of variables `vars={x,y}` we can generate a list of linear equations using the matrix equation `m.vars==b` which gives `{x+y,-x+y}=={1,2}`. How do I transform equations into `eqs={1-x,x+2}`? In other words how do I solve for `y = rhs` but only returning the rhs? I tried different things including picking parts with `Part` and `ReplaceAll` rules and transformations but none worked.

The reason I want equations in rhs form is that I figured out how to "visualize" linear equations using `Plot`. All other tutorials including Wolfram documentation and published books use `ContourPlot` or graphics primitives `Line` for this which I find too cumbersome for some of the simplest of functions. With `Plot` it is very easy to do `Plot[eqs,{x,-10,10}]`.

Here is my code to facilitate a solution...

    ClearAll[m,b,eqs,vars,x,y];
    vars = {x,y};
    m = {{1, 1}, {-1, 1}};
    b = {1, 2};
    eqs = m.vars == b;

the solution should be equivalent to this...

    eqs = {1-x, x+2};
    Plot[eqs, {x, -10, 10}]

[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/pcxaH.png