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2x + y = 6

6x + 3y = 18

Usually you can use elimination, substitution, graphing, matrices, etc. to find the answer to this system. If you use any of these methods (elimination and graphing in particular) you will see that these two equations are actually the same: multiply the first equation by three and you will see what I mean.

So picture it: graphing this system would essentially be drawing the same line twice. The two lines always overlap, so the equations share infinite solutions. Therefore the solution to the system is the whole line, or all the (x, y) points that satisfy 2x + y = 6.

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