Describe the different types of results that will occur when performing transformations on equations that have one solution no solution or infinitely many solutions

This is a very broad question. When performing rotations, if there was an infinite amount, there will now be 1 solution, and if there were no solutions, there will be one now. Vice versa. With transforming as in moving, one with no solutions might have an infinite amount, and one with a single solution will have a different solution

I can show you some equations

examples
one solution equaions
y=2x+3
y=3x+3
no matter how you move them, as long as you do not touch the slope, there will be only 1 solution

for no solution equations
y=2x+3
y=2x+4
paralel so never touch and no solution
but if we translated y=2x+3 up 1 unit, we get infinite solutions

for infinite it is the reverse of the 2 solution one
y=2x+3 and
y=2x+3
translating the bottom one down by 1 unit make no solution