# Thread: Solving simultaneous recurrence relations

1. ## Solving simultaneous recurrence relations

How to start the following problem that is asking to solve simultaneous recurrence relations:
An = 4 A(n-1) + 3 B(n-1)
[A subscript n = 4 * A subscript (n-1) + 3 * B subscript (n-1)]
Bn = 2 A(n-1) + 3 B(n-1)
[B subscript n = 2* A subscript (n-1) + 3* B subscript (n-1) ]

I know how to solve recurrence relations so I don't need help but what is confusing me is to solve simultaneous recurrence relations. How can I start?

Thank you for your time and any type of help you can provide me!
This is only a fictif example, so if anyone could provide me a solution, I will try to apply it to the real problem that I have to solve.

2. Originally Posted by precious_pearl13
How to start the following problem that is asking to solve simultaneous recurrence relations:
An = 4 A(n-1) + 3 B(n-1)
[A subscript n = 4 * A subscript (n-1) + 3 * B subscript (n-1)]
Bn = 2 A(n-1) + 3 B(n-1)
[B subscript n = 2* A subscript (n-1) + 3* B subscript (n-1) ]

I know how to solve recurrence relations so I don't need help but what is confusing me is to solve simultaneous recurrence relations. How can I start?

Thank you for your time and any type of help you can provide me!
This is only a fictif example, so if anyone could provide me a solution, I will try to apply it to the real problem that I have to solve.
$A_n = 4 A_{n-1} + 3 B_{n-1}$ .... (1)

$B_n = 2 A_{n-1} + 3 B_{n-1}$ .... (2)

From (2): $A_{n-1} = \frac{B_n - 3 B_{n-1}}{2}$ and it follows from this that $A_{n} = \frac{B_{n+1} - 3 B_{n}}{2}$.

Substitute both these expressions into (1) and solve the resulting recurrence relation for $B_n$.

### show examples solved by using simultaneous recurrence relations discrete mathematics?

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