Particular Solution of System of Constant Coefficient Linear 1st Order ODEs

Theorem
Consider the system of linear first order ordinary differential equations with constant coefficients:

Let $(1)$ and $(2)$ have the following $n$ initial conditions:
 * $(3): \quad y = y_0, z = z_0$

when $x = x_0$.

Then there exists exactly one particular solution of $(1)$ and $(2)$ which satisfies $(3)$.