Consider the following homogeneous first-order system of differential equations with the initial conditions x(0) = -5, y(0) = 0.

x' = 2x + 7y

y' = 5x - 2y

a. Convert the system to a single second-order differential equation and solve. The answer should have expressions for both x(t) and y(t). Show your work.

b. Solve the system using the eigenvalue method. Show your work.