Question about linear combination of two vectors

Question:

"What condition must be met by the two vectors of a basis such that any given vector can be expressed as a linear combination of these two vectors?"

Answer (from answer booklet):

"They must be linearly independent (or non-collinear)."

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Before checking the answer, I answered the exact opposite. My argument is that, when you combine two vectors in order to form another with a __linear__ combination, those two vectors had to be collinear in order for them to produce another vector in the same linear path (=same slope).

How am I wrong?