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I'm trying to graph a 1 dimensional object that curves in 3 dimensions. The only way I've ever been able to do this is with parametrics in Mac Grapher, or by graphing two 2 dimensional surfaces in 3 dimensions and manually looking at the intersection. Is there a tool that would allow me to graph just the intersection of two surfaces, i.e. the solution set of two equations?

To be more concrete, what I'm trying to graph is the solution set to this system of two equations:

x^2-y^2+z^2=2

xy+z=0

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