To find the general solution of the given system, we can use the method of elimination.
Multiplying the first equation by 2 and subtracting it from the second equation, we get:
2(dy/dt) - d/dt(2x) = 2(4x - 2y) - 2(2x - y)
Simplifying, we get:
d/dt(y - 2x) = 0
Integrating both sides with respect to t, we get:
y - 2x = C
where C is a constant of integration.
Substituting this expression for y into the first equation, we get:
dx/dt = 2x - (y - 2x) = 3x - C
This is a separable differential equation, which we can solve by separating the variables and integrating both sides:
(dx/x - (C/3)) = dt
Integrating both sides, we get:
ln|x - (C/3)| = t + K
where K is another constant of integration.
Solving for x, we get:
x(t) = (C/3) + Ae^(3t)
where A is a constant of integration.
Substituting this expression for x into the equation y - 2x = C, we get:
y(t) = 2(C/3) + Be^(3t)
where B is a constant of integration.
Therefore, the general solution of the given system is:
x(t), y(t) = (C/3) + Ae^(3t), 2(C/3) + Be^(3t)
where A and B are constants of integration, and C is a constant that determines the relationship between A and B.