The rectangular coordinate system is the basis for how we find locations on a map, for example (even though the earth is actually a sphere, this was a basis). I would say it is rather important.
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The origin is where the two intersect. This is where both number lines are 0.
A Cartesian coordinate system, or rectangular coordinate system, is a 2-dimensional coordinate system. The X-axis and Y-axis only intersect at one special point called the origin. This point has the coordinates of (0,0).Wikipedia has particulars, and a link is provided.
The coordinate system can be in any number of dimensions whereas the coordinate plane is a 2-dimensional concept.