Use the Laplace transform to solve the following initial value problem: x' = 12x + 4y, y -8x + e¹t x(0) = 0, y(0) = 0 Let X(s) = L{x(t)}, and Y(s) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s):

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