System Architecture Design Methodologies are like recipes for building complex systems. These methods provide a framework for architects to follow. They design the system for flexibility, simplicity, and consistent performance. Here are some common System Architecture Design Methodologies:

Monolithic Architecture: This approach builds the entire system as a single, self-contained unit. It is often used for smaller applications or proof-of-concepts.

Pros:

1. Since there is a single codebase, it makes it easier to develop, test, and debug.

2. Deployment is often faster and more straightforward.

3. It is relatively easier to optimize performance because all components are co-located.

Cons:

1. A single codebase simplifies deployment, but hinders scaling. As the application grows, adding resources forces you to scale the entire application.

2. Components are tightly coupled. This makes it hard to change them without affecting the whole system.

3. It has a single point of failure.

Microservice Architecture: In this approach, a single application consists of many small services. They are independent and loosely coupled. Each service is designed to perform a specific task.

Pros:

1. You can easily scale up or down each microservice. You do this depending on if demand increases or decreases.

2. If a particular microservice is down, the rest of the system will not be affected.

3. Maintaining a smaller, independent component is easy. It is easier than making changes in a monolith repository.

Cons:

1. Managing multiple services can be more complex than deploying a single application.

2. Tracing problems gets harder. You might need to search through many services to find the problem.

3. Services communicating over a network can increase latency. But, this may not be true in a monolith architecture.

Service-Oriented Architecture (SOA): SOA is a middle state. It is between monolith and microservices architectures. SOA takes a hybrid approach. It keeps some coupling between systems, but not as much as in a monolith. SOA typically involves large, complex services. They have a lot of business logic. Microservices are smaller and focused. They perform a specific task or function.
Pros:

1. Easier to implement than a microservice, as it requires less complex infrastructure.

2. SOA is well-suited for small-scale applications that don't require much scalability.

3. SOA has a centralized management approach, which makes governance easier.

Cons:

1. SOA services are often scaled vertically. This makes it hard to scale them horizontally.

2. SOA services are tightly coupled, making it harder to make changes.

3. The maintenance cost for SOA services could be higher if not set up properly.