You can pick a blue and a yellow and a proportion at which to mix them which will produce white, but for any two primaries you pick, there are a multitude of colors you can't represent. For example, if your basis is blue-yellow as you suggest, then you can't represent red or green (and an infinity of other colors off-axis).
Fundamentally the chromaticity diagram[1] is 2D (with a third axis for intensity). You need to mix at least three points to span the space of the plane.
