eliminate eliminates the given variables from a set or list of equations.

The result of this elimination is an expression sequence of lists.  Each list represents a possible elimination of the given variables.

The first component of each solution is a set of equations, where the left-hand side of these equations is a variable (one of the variables in varset) and the right-hand side is its corresponding value.  The second component of each solution is the set of remaining equations once the varset have been eliminated.

$\mathrm{eliminate}\left(\left\{x^3-y^{2}x+xy-3\,x^2+y^2-1\right\}\,x\right)$

$\left[\left\{x=\frac{3}{-2y^2+y+1}\right\}\,\left\{4y^6-4y^5-7y^4+6y^3+4y^2-2y+8\right\}\right]$

$\mathrm{eliminate}\left(\left[x+\sin \left(y\right)\,3\cos \left(x\right)+xy\right]\,x\right)$

$\left[\left\{x=-\sin \left(y\right)\right\}\,\left\{3\cos \left(\sin \left(y\right)\right)-\sin \left(y\right)y\right\}\right]$

$\mathrm{eliminate}\left(\left\{3\sin \left(y\right)z+5xy\,3y{z}^{2}x+\cos \left(x\right)z\,\exp \left(x+z\right)\right\}\,x\right)$

$\left[\left\{x=-\frac{3\sin \left(y\right)z}{5y}\right\}\,\left\{z\left(-9\sin \left(y\right)z^2+5\cos \left(\frac{3\sin \left(y\right)z}{5y}\right)\right)\,{\ⅇ}^{-\frac{z\left(3\sin \left(y\right)-5y\right)}{5y}}\right\}\right]$

$\mathrm{eliminate}\left(\left\{x+z\,3y^{2}z+5xy\,5z+3y{z}^2+xy\right\}\,\left\{x\,y\right\}\right)$

$\left[\left\{x=-z\,y=-\frac{5}{3z-1}\right\}\,\left\{25z\left(2+3z\right)\right\}\right]$