Graphing of Systems

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Section 3.3 Graphing of Systems

Since each equation implicitly defines a function, we can use implicit_plot to graph each equation in 2D-space.

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We can also plot a point whose coordinates are the ones given in the solution.

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Now, the full plot with the equations, the solution, and a legend.

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We can plot equations in 3D-space using implicit_plot3d. Here is an example with $\textbf{Case I}\text{:}$

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Here is the same method with $\textbf{Case II}\text{:}$

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By rotating the graph, we can visualize the infinitely many solutions of this system, represented by the line where the three planes intersect.

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Here is another example with $\textbf{Case III}\text{:}$

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In this last case, we can observe that two of the planes are parallel, so there is no intersection among the three planes.

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