Conisder the (2X2) system
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Dr.Peterson
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When I don't know what to do, I sometimes try playing with the problem using specific numbers. Pick some numbers for the a's and b's, and try doing what they ask. That may give you ideas for what to do in general.
It may also help if you tell us what you have been learning recently, since that may suggest what we should or shouldn't expect of you.
Dr.Peterson
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Okay; I suppose you haven't been introduced to matrices yet, or to specific things to do with them; I wouldn't expect you to be using those ideas anyway.
Please try what I suggested. If, say, the given equations were 2x + 3y = 4 and 3x + 1y = 2, where (2)(1) - (3)(3) = -7 which is not 0, how would you eliminate the coefficient of x in the second equation? And what would you do differently if the first 2 were replaced with 0?
Then do the same things with unspecified parameters, as given.
The more though you show, the easier it will be to help you.
Please try what I suggested. If, say, the given equations were 2x + 3y = 4 and 3x + 1y = 2, where (2)(1) - (3)(3) = -7 which is not 0, how would you eliminate the coefficient of x in the second equation? And what would you do differently if the first 2 were replaced with 0?
Then do the same things with unspecified parameters, as given.
The more though you show, the easier it will be to help you.
logistic_guy
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As an expert in differential equations and matrices, I would suggest to move the first system to a Matrix notation. Then you can easily show that system \(\displaystyle 1 \equiv \) system \(\displaystyle 2\) by using Matrix properties.
