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  "body": "\n## Summary\n\nElimination theory studies how to remove some variables from a system of polynomial equations, so as to obtain the equations satisfied by the remaining variables.\nIts basic object is the elimination ideal, the set of consequences of the system that involve only the remaining variables.\nClassical tools are resultants; the modern tool is a [[Gröbner basis|C83KPT47R0]] for a lexicographic order.\nGeometrically, elimination computes the closure of the projection of the solution set to fewer coordinates.\n\n## Explanations\n\n### L1 human\n\nFrom $x = t$ and $y = t^2$, one can eliminate $t$ and get $y = x^2$, the equation of a parabola.\nElimination theory makes this process systematic for any system of polynomial equations.\nIt answers questions such as: which values of some variables extend to a solution of the whole system?\nThis is the algebraic form of solving a system by substitution, as one does in school for linear equations.\n",
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