why eliminate can not recover the original set of equations

Question:why eliminate can not recover the original set of equations

Posted: ComputerUser 535

September 17 2014

with(Groebner):
eq1 := a+b*c;
eq2 := a*b*c+a;
eq1a := Homogenize(eq1, h);
eq2a := Homogenize(eq2, h);
eliminate([eq1a,eq2a], h);

after eliminate not equal to eq1 and eq2

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