Find a parametric representation of the solution set of the linear equation. (enter your answer as a comma-separated list of equations. use s and t as your parameters.) −8x + 5y − 4z = 1

Step-by-step explanation:

There are at least 3 ways to do this problem, let us do it one way and then I'll explain how to do it from another approach. First of all let's begin by solving the linear equation for x. We get the following:

We can see that and   could act as free variables as we have no conditions or restrictions on the values of x and y. Normally one would see such restrictions by adding more equations as in a system of equations. That is why we can call   and   free variables.

If we for instance let   and   where   then we can write the linear equation as follows:

and are calle parametric variables.

but there’s no any figure there!