What is the best way to plot the solution to a system of equations in 2D and 3D, where Mathematica does as much of the heavy lifting as possible?
I'd like to give Mathematica a system, say, x==y and y-x==0 and have Mathematica give me a 2D plot showing points (1,1) and (-1,-1). Or give Mathematica the system x^2+y^2+z^2==1 and x==y and get a 3D plot of a circle about the origin in the x=y plane.
I know how to produce the plots using ParametricPlot functions, but my hope is that Mathematica can give me a easier way to quickly visualize solutions to systems of equations more complicated than the examples above.
An even better visualization would be a manipulatable plot that toggles through the equations and their intersection.
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Hi, Moderation Team.
I realize most posts are about executing a specific approach. I could have asked how to manipulate results from Solve so they can be used as an argument for ContourPlot and ContourPlot3D. I can probably figure that out on my own. But I don't know if that's even the best approach.
Ultimately, I'd like to write a manipulatable function to visualize geometric objects defined by systems of real-value polynomial equations. I've been reading about affine varieties. If I get closer to my goal, I will probably be back here with the kind of specific coding questions you're used to. But right now, all I want is advice on the most useful functions to use.