The solution set contains the origin because if you plug x=y=z=0 into your equations, each of them becomes 0=0 which is true. If you have nonzero constant terms in one or more of your equations, this will not be the case, and you need to offset the span by a known particular solution, if there are any solutions at all.
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The solution set contains the origin because if you plug x=y=z=0 into your equations, each of them becomes 0=0 which is true. If you have nonzero constant terms in one or more of your equations, this will not be the case, and you need to offset the span by a known particular solution, if there are any solutions at all.
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