Here are the steps for solving the system of equations:

1. $x - 2y = -19$
2. $y = -5x + 1$
3. $x + 3y = 14$
4. $x - 3y = -8$

Substitute equation (2) into equations (1), (3), and (4):

1. $x - 2(-5x + 1) = -19$
2. $x + 3(-5x + 1) = 14$
3. $x - 3(-5x + 1) = -8$

Solve the system to find values for $x$ and $y$. Let me proceed with the calculations.

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Let me know if you'd like the detailed solution steps or have any questions. Here are a few related questions:

1. How do we solve a system of equations using substitution?
2. What is the graphical representation of this system of equations?
3. How do we check for consistency in a system of equations?
4. What is the importance of the substitution method in solving linear equations?
5. How do you solve systems of equations with more than two variables?

Tip: Always check for possible contradictions or inconsistencies after solving a system to ensure a solution exists.