Cramer's theorem (algebraic curves)

So, imagine you have a piece of paper with a bunch of dots on it. These dots can be connected together to make a shape. This shape is called a curve.

Now, some curves are really special. They have a property called degree, which basically means how many times the curve crosses itself. If the curve doesn't cross itself at all, it has degree 0. If it crosses itself once, it has degree 1.

Cramer's theorem helps us understand how these special curves behave. It says that if you draw a line through the curve, the line will intersect the curve at a certain number of points. And the number of points the line intersects the curve is always equal to the degree of the curve!

So if you have a curve with degree 2, and you draw a line through it, the line will always intersect the curve at 2 points. If you have a curve with degree 3, the line will always intersect the curve at 3 points.

This might seem like a simple idea, but it's actually really powerful. It can help us solve lots of math problems, and understand how curves behave in different situations.