Give the solution set of 216x − 144y + 24z − 22 = 2 in parametric form

The given equation is a linear equation in three variables x, y, and z. To express the solution set in parametric form, we can express two variables in terms of the third variable.

Let's express x and y in terms of z.

First, we can simplify the equation by dividing all terms by 2:

108x - 72y + 12z - 11 = 1

Then, we can rearrange the equation to solve for x:

108x = 72y - 12z + 11

Divide through by 108:

x = (2/3)y - (1/9)z + 1/108

Similarly, we can rearrange the equation to solve for y:

72y = 108x + 12z - 11

Divide through by 72:

y = (3/2)x + (1/6)z - 11/72

So, the solution set in parametric form is:

x = (2/3)t - (1/9)z + 1/108 y = (3/2)t + (1/6)z - 11/72

where t is a parameter.