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You can still solve it using the same method. However, you would most likely need to know the order of the other species to solve for it or would need more algebra to go through the problem.
I don't think this is the easiest way, but one important distinction is that different orders have differently shaped graphs of concentration vs time. You can tell what the order is by observing which concentration vs. time graph is linear. For first order reactions, ln[A] vs. time is linear. For second order reactions, 1/[A] vs. time is linear. For zeroth order reactions, [A] vs time is linear.
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