Question

"Write a system of equations in three variables that has a single solution of (-1, -2, -3)"

The first equation that I made was x+y+z = -6, but I'm not sure on how to continue with it.

Answer 1

How would I write a system of equations in three variables that has no solution?

Answer 2

That's a great start. You could continue by creating some more true statements based on the given values;
e.g. 4(-1) - (-2) - (-3) = 1, so 4x-y-z = 1
etc.