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Plot the solution to a system of equations

Posted 2 months ago
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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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Your post is vague. Please describe your subject extensively providing the details, examples of required code and expected output, and other relevant ideas, so it is clear what exactly you are looking for.

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.

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