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The x and y coordinates are plotted on the Cartesian plane.
That would depend on the given system of linear equations which have not been given in the question
It means the position [of an observation] in an ordered data set.
As ordered sets of numbers - pairs for coordinates in a plane, triplets for coords in 3D space, and so on for higher dimensions.
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.