Graph of 3 variable system

can some one sketch the graph for 3x -4y +2 z=24 is it going to be rectangular plane or triangular?
I am confused. These are 3 points if connected you get triangle

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There are an infinite number of sets of (x, y, z) that will satisfy the equation.
They will all lie on the same plane.
That’s very difficult to graph in 3D.

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What is the shape of the plane? In one you tube video it said it is rectangle in another it is triangle

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A plane is a flat 2D surface with infinite dimensions.

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Hello @Hassan_Mohamed6 ,

I’ll further elaborate on the explanation to clarify your doubt.

Consider the simple equation:

x + 3 = 10

In this case, there’s only one solution, which is when x equals 7, correct?

Now, let’s consider the following equation:

x + y = 10

Here, there are infinite possible solutions, such as 1 + 9, 2 + 8, 3 + 7, and so on. These solutions form an infinite set that can be represented on a Cartesian plane with the x and y axes, that is, on a two-dimensional surface represented by a line.

For the more complex equation:

3x - 4y + 2z = 24

The reasoning is similar. This equation also has infinite possible solutions. It’s important to remember that if the number of pieces of information (equations) is smaller than the number of unknown values (variables), it may indicate the possibility of infinite solutions or even no solution. The analysis will depend on the specific system, and this concept is also covered in the course.

In any case, here is the image of the graph of the equation you provided represented on the plane.


Thanks martins. I liked your graph.
Can you check this video. It says the plane is triangular. How do you reconcile it with yours?

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What is the time mark in that video where this issue is discussed?

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The person in the video is plotting the three points where a solution intersects each axis.
That defines the plane.

The triangle they’ve drawn just shows where the plane intersects the graph axes. But the plane extends infinitely in all directions. The only significance of the triangle is that it lies in that plane.

I’ve marked up a screen capture to show this.


Thank you for the I understand

can someone please sketch the graph for 6z-5y+z=62 ,is it going to be a rectangular plane or triangular?

We cannot sketch a plane. It is flat and infinitely large.

the plane is infinite, so we can create auxiliary points on the axes to get an idea of its behavior. Here’s the sketch, but I made a correction to the equation to have three variables (6x - 5y + z = 62).