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Here's my problem:

I have some corresponding values for two variables a and b.

I also know that

[tex]a_n = 2a_{n-1} + b_{n-1}[/tex]

and

[tex]b_n = b_{n-1} + a_n[/tex]

for all a and b.

I need to find functions [tex]f_1[/tex] and [tex]f_2[/tex] in terms of n so that [tex]f_1(n) = a_n[/tex] and [tex]f_2(n) = b_n[/tex]

I don't really know where to start. I tried recombining the first two equations in myriad ways but I didn't get anywhere there. I have figured out that this would be pretty tough without the sample values to generate the others, and that the answers will be in general form because n = 1 could refer to any of the pairs of values, although all of them can be generated from a single pair. What do I do?

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# Two functions in two variables

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