In each of Problems 1–22, use the method of elimination to determine whether the given linear system is consistent or inconsistent. For each consistent system, find the solution if it is unique; otherwise, describe the infinite solution set in terms of an arbitrary parameter t (as in Examples 5 and 7).

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Example 5 If, instead of the system in (9), we had begun in Example 4 with the system 2x + 6y = 4 3x + 9y = 6 and performed the same operations, we would have obtained, instead of (10), the system x + 3y = 2 0=0. Here, 0 = 0 is shorthand for the equation (11) (12) 0x + Oy = 0, which is satisfied by all values of x and y. In terms of restrictions or conditions on x and y, one of our original two equations has in effect disappeared, leaving us with the single equation x + 3y = 2. (13)