Final answer:
To convert the second-order differential equation into a first-order system, a new variable v is defined as dy/dt, resulting in a system of two first-order equations: dv/dt = -5v - 6y and dy/dt = v.
Step-by-step explanation:
To convert the second-order differential equation d2y/dt2 + 5dy/dt + 6y = 0 into a first-order linear system, we introduce a new variable to reduce the order of the differential equation. Let's create a variable called v such that v = dy/dt. This allows us to rewrite the original second-order equation in terms of v and y.
The system of first-order equations will be:
This first-order system can be represented in matrix form or solved using methods for systems of first-order linear differential equations.