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