Why doesn't solve give any indication that there can be a non-trivial solution to this system of two linear equations?

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We have two equations. Image may be NSFW.
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Maple says the only solution is the trivial solution.

If we check the determinant of the matrix of the system we see it can be zero for certain values of Image may be NSFW.
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If Image may be NSFW.
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For example, subbing the first value above into the equations and solving Maple gives us non-trivial solutions.

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Why didn't Maple give us any indication that there could be non-zero solutions in the first call to Image may be NSFW.
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