so dear community, here is my second question.
assume we have a system, where
$A_1 x + B_1 y = C_1 $
$A_2 x^2 + B_2 y^2 = C_2 $
$A_3 x^3 + B_3 y^3 = C_3 $
etc.
can this system be solved?
if yes, i would appreciate some guidance.
so dear community, here is my second question. assume we have a system, where $A_1 x + B_1 y = C_1 $ $A_2 x^2 + B_2 y^2 = C_2 $ $A_3 x^3 + B_3 y^3 = C_3 $ etc. can this system be solved? if yes, i would appreciate some guidance. 


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The first two equations determine your $x, y$ up to finite indeterminacy, so your system is generally overdetermined. To solve the first two equations, the quadratic formula works well. 

