The Cartesian system, also known as the rectangular coordinate system, is a fundamental mathematical system used to represent points and geometric shapes in a two-dimensional or three-dimensional space. It was developed by the French mathematician and philosopher René Descartes in the 17th century.

The Cartesian system is based on two perpendicular lines, called axes, which intersect at a point called the origin. The horizontal axis is conventionally labeled as the x-axis, while the vertical axis is labeled as the y-axis. In a three-dimensional Cartesian system, there is an additional axis called the z-axis, which is perpendicular to both the x-axis and y-axis.

The key features of the Cartesian system include:

1. Coordinate Points:
- Any point in the Cartesian system can be represented by a set of numbers called coordinates.
- In a two-dimensional Cartesian system, a point is represented by an ordered pair (x, y), where x represents the distance along the x-axis and y represents the distance along the y-axis.
- In a three-dimensional Cartesian system, a point is represented by an ordered triple (x, y, z), where x, y, and z represent the distances along the x-axis, y-axis, and z-axis respectively.

2. Cartesian Plane:
- The Cartesian system divides the plane into four quadrants, numbered counterclockwise from the upper right quadrant as I, II, III, and IV.
- The origin (0, 0) is the point of intersection of the x-axis and y-axis.
- The positive x-axis extends towards the right, while the positive y-axis extends upwards.
- The negative x-axis extends towards the left, while the negative y-axis extends downwards.

3. Distance and Slope:
- The distance between two points in the Cartesian system can be calculated using the distance formula.
- The slope of a line passing through two points can be calculated using the slope formula.

4. Graphing:
- The Cartesian system is widely used for graphing functions and equations.
- The x-axis represents the independent variable, while the y-axis represents the dependent variable.
- Graphs of functions and equations can be plotted using points, lines, curves, and surfaces on the Cartesian plane.

In summary, the Cartesian system, also known as the rectangular coordinate system, is a mathematical system used to represent points and geometric shapes in a two-dimensional or three-dimensional space. It provides a standardized way to describe and analyze mathematical relationships and is widely used in various fields, including mathematics, physics, engineering, and computer science.