How to plot a nonlinear system of 3 equations with 3 symbolic variables in MATLAB?

Question

I don't have a lot of experience with Matlab. I know that you can plot equations with 2 variables like this:

ezplot(f1)
hold on
ezplot(f2)
hold off;

How would you plot three equations with three symbolic variables?

An example system would be:

x^2+y^2+z^2-1=0
2*x^2+y^2-4*z=0
3*x^2-4y+z^2=0

It would be ideal if there was a way to plot any system of 3 equations.

Answer 1

I believe ezsurf comes close to what you want. You would first have to solve each equation for z, then make a function for that equation and plot it with ezsurf. Here's how to do it with your first equation from above:

func1 = @(x, y) sqrt(1-x.^2-y.^2);
ezsurf(func1);

This should display the upper half of a sphere.

To display all three equations together, you can do the following:

func1 = @(x, y) sqrt(1-x.^2-y.^2);
func2 = @(x, y) 0.5.*x.^2+0.25.*y.^2;
func3 = @(x, y) sqrt(4.*y-3.*x.^2);
ezsurf(func1, [-1 1 -1 1]);
hold on;
ezsurf(func2, [-1 1 -1 1]);
ezsurf(func3, [-1 1 -1 1]);
axis([-1 1 -1 1 0 1]);

and the resulting plot will look like this:

By rotating the plot, you will notice that there appear to be two points where all three surfaces intersect, giving you two solutions for the system of equations.

Answer 2

"hold on" just says to not erase existing lines & markers on the current axis. you should just be able to do

ezplot(f1);
hold on;
ezplot(f2);
ezplot(f3);
hold off;

I've never used ezplot so can't help you with that one.