Simultaneous equations
Python 3, 250

I reuse the code for parsing the input for each of the "coefficients" of x, y, and "=" by putting it into a string and multiplying it the right number of times.

For the "coefficient of =" case to work (absence means 0, not 1, like for x and y), the last "0" of the input has to be thrown away (and then magic takes over...).
Makes heavy use of short circuiting in logic expressions, and of False==0.

Uses Python's feature of leaving off trailing zeros of floats (finding out if the solution is an integer is still necessary).

exec((("R=input()[:-1];"+"*_,R=I,*_=R.split(%r);%s=R!=I and int(I in'+-'and I+'1'or I);"*3)*2)%tuple("xXyY=Cxxyy=c"))
d,u,v=X*y-Y*x,C*y-c*Y,X*c-x*C
print(d and"x=%s, y=%s"%(u%d and-u/d or-u//d,v%d and-v/d or-v//d)or"UDnesgoelnvearbaltee"[u==v==0::2])