Final answer:
The question pertains to solving a system of linear differential equations by elimination, a method that requires identifying knowns, systematically combining equations to isolate one variable, and then substituting back to find the other variable.
Step-by-step explanation:
When solving the given system of differential equations by systematic elimination, we start by identifying the known variables and relations. The equations provided seem to be a form of a linear differential equation system. The goal is to isolate one variable and then substitute back to find the other. However, it appears that the question contains a typo or is incomplete, as the equations given do not form a clear system. In practice, one would first correct any typos or clarify the system of equations. Typically, we can solve these systems by expressing one variable in terms of the other, and using substitution to reduce the system to a single differential equation that can be solved directly.
For instance, if we had a system like Dx - y = f(t) and (D + 5)x + (D + 5)y = g(t), we would look for ways to eliminate one variable by combining the equations. This often requires multiplying the equations by constants that will allow the terms of one of the variables to cancel when the equations are added or subtracted.
After finding the solution for one variable, we substitute this back into one of the original equations to find the solution for the other variable. Finally, solving for x(t) and y(t) provides the general solutions to the system.