Question

Write a system of equations, three equations/three unknowns, that has (1, 2, 3) as the
solution.

for this can I just write any random coefficient and then put that as equal to 1,2 or 3? or if not what type of math would I use?

Answer 1

yup, your first suggestion is correct
just make up something like
3x - 2y + 5z = ....
3(1) - 2(2) + 5(3) = 3-4+15 = 14

so 3x - 2y + 5z = 14 could be one of your 3 equations

just make up 2 more like that