solving one variable with two equations

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No, this is also in Maxima.

(%i1) solve([x+y=2,y=x],[x,y]);
(%o1)                          [[x = 1, y = 1]]
(%i2) solve([x+y=2,y=x],[x]);
(%o2)                                 []

I suppose you were expecting [x=1]... I don't know how to get Maxima to do that.

In your first version, solve views y as a known parameter (that Sage does not assume up front to be $-2$) and not a variable. So, the system doesn't have a solution.

In your second version, solve views y as a variable and solves for it.