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You provided the following system of three linear equations:

\[
\begin{align*}
-3a - b - 3c &= -8 \\
-5a + 3b + 6c &= -4 \\
-6a - 4b + c &= -20
\end{align*}
\]

I will now solve this system of equations using substitution or elimination. Let's proceed with the solution.

### System of equations:

\[
1) \quad -3a - b - 3c = -8
\]
\[
2) \quad -5a + 3b + 6c = -4
\]
\[
3) \quad -6a - 4b + c = -20
\]

I'll solve it now.The solution to the system of equations is:

\[
a = 2, \quad b = 2, \quad c = 0
\]

Would you like a detailed explanation of the steps or have any further questions?

Here are five related questions you can explore next:
1. How can this system of equations be solved using the elimination method?
2. What happens when a system of equations has no solution?
3. How can I represent this system graphically?
4. How does substitution work in solving systems of equations?
5. What are the applications of systems of equations in real-world problems?

**Tip:** When solving systems of equations, always check if the system has a unique solution, infinitely many solutions, or no solution by examining the determinant or the relationships between the equations.

Solve the system of equations: -3a - b - 3c = -8, -5a + 3b + 6c = -4, -6a - 4b + c = -20.

Learn how to solve the system of linear equations with three variables: -3a - b - 3c = -8, -5a + 3b + 6c = -4, and -6a - 4b + c = -20. This problem covers algebraic concepts including the elimination method, substitution method, and matrix method. Suitable for students in Grades 9-12.

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