Systems of polynomial inequalities

So imagine you have a bunch of crayons, and you want to color in a big square. But you don't want to color in some parts of the square because maybe your mom told you to leave some parts white.

With systems of polynomial inequalities, you have a similar situation. Instead of a square and crayons, you have some equations that are related to each other. Each equation might have different rules for what can be colored in or not.

You want to find all the points on a graph that fit all the rules from each equation, kind of like how you want to color in all the parts of the square that aren't blocked off. These points might make a special shape, like a square or circle or something else.

Sometimes you have to use more than one equation to find all the points you're looking for. But in the end, you can use these systems of polynomial inequalities to help you figure out which points on a graph you should color in and which ones you shouldn't based on the rules each equation gives you.