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Chemistry - Rate Equations Help

Hello, this is the question including my workings:
6884848D-21F7-4BA1-9CB6-6F683A6D2807.jpg.jpeg

My question is about part (c) where it asks me to determine the order of the reaction with respect to A and order of the reaction with respect to B. I first tested the given information in my head and 2 and 0 respectively seemed to make the factor scaling true however this was using a process of trial and error.
I tried to establish a more rigorous method as shown at the bottom to deduce what x and y (the respective orders of the reaction with respect to their reactants A and B) by firstly creating a table with initial concentrations and rates then constructing 3 equations based on the rate equation and constructing a further two equations in x and y by cancelling the k, a and b out as they were proportionality constants. I tried solving for x and y however I yield two values which:
(A) are negative and the orders I have come across are generally 0, 1 and 2
(B) non-integer, I understand if they were close approximations but these are based off proportions as oppose to actual experimental data
(C) not equal to the trial and error calculated values of 2 and 0 respectively

I have tried looking for an error in the rigorous method and can’t find anything. I’m not sure if I’ve made an error in the approach but my question is; how do I deduce the orders using a method instead of trial and error?
Thanks

Edit:
I have tried to zoom in on the page in two separate images:
Attachment not found

and
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(edited 3 years ago)
Your numbers seem fine. There isn’t much of a rigid method for this as you don’t have the table. But this is pretty much the only logical solution hence why it isn’t many marks and doesn’t ask you to explain why like many questions do. It’s probably put in as an easy question. Your units look good too.
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BrandonS15
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Original post by DanaH111
Your numbers seem fine. There isn’t much of a rigid method for this as you don’t have the table. But this is pretty much the only logical solution hence why it isn’t many marks and doesn’t ask you to explain why like many questions do. It’s probably put in as an easy question. Your units look good too.


I realised the error lied on the direct substitution where I’ve accidently flipped the fraction when I shouldn’t have (4c/c) line. Continuing with the corrected fraction yields y=0 and x=2. Alternatively using experiment pairs 2 and 1 and (3 and 1) yields y=0 and x=2 too, although its much more simplier to infer the answer. Also knowing there isn’t pairs of experiments that have equal concentrations hints that one of the reactants has order 1 too.

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