Plotting systems of linear equations with 3 variables

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For the threejs viewer, you can use the argument opacity, i.e. replace alpha=0.3 by opacity=0.3 in implicit_plot3d; see the list of threejs options.

Hello, Thank you. That helped. What I was hoping to do was to have 3 distinct lines (or curves) rather than planes. The code did work though. I'm not familiar with viewers.

x, y, z = SR.var('x y z')
a, b, c = [2*x + 3*y - z == 15, x - 3*y + 3*z == -4, 4*x - 3*y - z == 19]
xx = (x, -10, 10)
yy = (y, -10, 10)
zz = (z, -10, 10)
pa = implicit_plot3d(a, xx, yy, zz, color='blue', alpha=0.3)
pb = implicit_plot3d(b, xx, yy, zz, color='red', alpha=0.3)
pc = implicit_plot3d(c, xx, yy, zz, color='green', alpha=0.3)
p = a + b + c
show(pa + pb + pc)

Taken one by one, each of the equations in your system have a set of solutions which is a plane (in the same way that if you say $z = 0$, the solution set is the whole $xy$-plane at altitude zero, so $x$ and $y$ can take any value).

If you take the equations two by two, then you get three lines: if some triple $(x, y, z)$ satisfies both (a) and (b), the corresponding point is both in plane (a) and plane (b), so it lies on the line which is the intersection of these planes. So, (a) and (b) give a line, (b) and (c) give another one, and (c) and (a) give a third one. Are those the lines you wanted to plot?

Thank you for your patience and help.

The goal is to create and image like the one at this link ( 3d Image so I can show a classroom of middle school and/or high school students what the solution to a system of linear equations that has 3 variables looks like. This abstraction can be very hard for students and me too.

@SteveF: one thing to understand is that:

• the solutions to the equation $2x + 3y - z = 15$ form a plane (not a line),
• the solutions to the equation $x - 3y + 3z = -4$ form a plane (not a line),
• the solutions to the equation $4x - 3y - z = 19$ form a plane (not a line).

In your drawing, what are the three colored lines?

Hello, Thank you for responding. Can you point me to a resource that shows how to create a list of points. And then another resource that shows how to plot with point3d(L)?

I use SageCell.

Thank you.