System of three coupled LDEs

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I have three equations, with X, Y and Z being time-dependent and all others being constant parameters:

X’ = aX + bY + m ; Y’ = cX + dY ; Z’ = eX + fY + n

I arrived at the above set of equations after reducing Z as a function of X and Y. (Z = constant - X - Y)

How do I arrive at the solution for this system?