I am struggling to find a way of solving the following equation (simplified 
example)
```
f = x+1
g = 2*x+1
expr = a*f + b*g - 1
solve(expr, (a, b))
```
I would like to have `a=2`, `b=-1` which make `expr` identically zero.

I am interested in polynomials with higher powers: at the moment, I derive 
with respect to x, subs 0 for x, accumulate the result as column in a 
matrix and solve the linear problem associated. This method works for 
univariate polynomials, but it become impractical for multivariate linear 
systems, which is my ultimate goal, because of the need to derive with 
respect to all mixed terms x^m*y^n. (I also could not find a way of 
collecting the coefficients of the terms x^m*y^n.)

Is there a way to solve these linear problems?

Thank you,
michele

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