What does the pair of equations y = 4, z = 8 represent? in other words, describe the set of points (x, y, z) such that y = 4 and z = 8?

We want to see what a pair of equations (two fixed values for variables) means.

We will see that these equations are actually describing a line parallel to the x-axis.

Now, let's see why:

In 3 dimensions we have points of the form (x, y, z)

Now we have two equations:

Then our points are of the form (x, 4, 8)

Is ratter easy to see that this is a line, this goes through all x-values, but the z and y-values are fixed.

Then the set of the points (x, 4, 8) is just a line parallel to the x-axis.

(Similar to how in two dimensions we say that x = a is a vertical line, and y = b is a horizontal line, here we are doing the exact same thing but in 3 dimensions)

If you want to learn more, you can read:

link

The set of points (x, 4, 8) is a line parallel to the x-axis through the point (y, z) = (4, 8) in the (y, z) plane.

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step-by-step explanation: