Consider the following system of differential equations: dx dt - x + y = 0, dy dt + 4x + 2y = 0. (i) Write the system in matrix form and find eigenvalues and eigenvectors to obtain particular solutions for r(t) and y(t) which satisfy the initial conditions (0) = 8 and y (0) = 5. (ii) Use the method of elimination to verify the general solution of part (i).

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