2021 JMPSC Invitationals Problems/Problem 4

Problem

Let and be sequences of real numbers such that , , and, for all positive integers , \begin{align*} x_{n+1}+y_{n+1} &= 2x_n + 2y_n,\\ x_{n+1}-y_{n+1}&=3x_n-3y_n. \end{align*} Find .

Solution

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