roots - How to find solutions for four polynomial equations with four unknown variables using RESULTANT THEORY?

Can I use resultant theory (or polynomial resultant method) to find solutions for FOUR simultaneous polynomial equations with FOUR unknown variables?

So far, I could only find examples which uses TWO equations having TWO unknown variables. I could also see an example of THREE unknown variables & THREE equations, but in that the first unknown was easily expressed as a function of other two variables.

The cases that I have come across for polynomials $f_1, f_2, ..., f_n$ are

A) Solve: $f_1(x_1, x_2)=0$ and $f_2(x_1, x_2)=0$

B) Solve: $f_1(x_1, x_2, x_3)=0$ and $f_2(x_1, x_2, x_3)=0$ and
$x_1=g(x_2, x_3)$. Here, g(.) is known

I am looking for procedure/example for solving using resultant method cases like these:

C) Solve: $f_1(x_1, x_2, x_3)=0$ and $f_2(x_1, x_2, x_3)=0$
and $f_3(x_1, x_2, x_3)=0$

D) Solve: $f_1(x_1, x_2, x_3, x_4 )=0$ and $f_2(x_1, x_2, x_3, x_4)=0$
and $f_3(x_1, x_2, x_3, x_4)=0$ and $f_4(x_1, x_2, x_3, x_4)=0$

Thank you in advance for your kind help.