What does it mean for an equation to have no solution or infinite solutions? how does the equation appear when those are the outcomes?

Ok so  if a system has no solutions, that means that no value will make it true

infinite solutions means that all numbers wil make the system true

example of no solution

a simplification that gives you
3=0
that is false so no solution

example of infinite
if after simplify you get
x=x
you can put all numer for x and get right answer

the simplified form of an equation with no solution will be in the form a=b where a is not equal to b, basically it gives you an obviously false statement like 3=4

simplified form on an equation with infinity solutions would end up with variable=variable or x=x or y=y

Figure it out your self