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