2. For the system of equations: dx = a11x + a12y, dt dy a21x + az2y. dt First, review lecture notes to see how we eliminate one variable to arrive at a single second-order equation. Then find the characteristic equation and solve the eigenvalues of the equation. Once x(t) is found, y(t) can be found by setting 1 dx - a11x) y(t)= (a12 # 0) a12 dt By using the above method, find solutions for the following systems: (a) dx = -4x + y, dt dy = 3x. dt

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