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Linear system has a proportional slope, which gives the system a straight line. And, a non-linear system has a non-proportional slope, which is represented by a non-straight line (usually a curved one). Feel free to edit if you think this is not to the point.
No, it is a linear transformation.
A system of linear equations that has at least one solution is called consistent.
No....not necessary
there is no linear equations that has no solution every problem has a solution