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You can write ordered pairs as ratios to determine if two sets of ordered pairs form a linear or non-linear relationship. In a table of x,y values, the ordered pairs are listed as the x value first, then the corresponding y value. Remove from the table and write as a ratio of x over y, (or y over x, if you like). In a linear relationship, all the ratios of x over y, (or y over x) are equivalent.
That would depend on the given system of linear equations which have not been given in the question
The x and y coordinates are plotted on the Cartesian plane.
As ordered sets of numbers - pairs for coordinates in a plane, triplets for coords in 3D space, and so on for higher dimensions.
There is no such thing. One number is one number.Structures with more than one number include sets (if the sets happen to be made up of numbers), and ordered pairs.