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The problem asks to determine which value is **not** contained in the solution of the system of equations. The system is as follows:

\[
\begin{align*}
a + 5b - c &= -20 \\
4a - 5b + 4c &= 19 \\
-a - 5b - 5c &= 2
\end{align*}
\]

The options provided are the following values of \( c \):
1. \( c = -2 \)
2. \( c = 2 \)
3. \( c = 3 \)
4. \( c = -3 \)

We will solve this system of equations to find the correct value of \( c \) and check which one is not a solution. Let's solve the system step by step.The solution to the system of equations is:

\[
a = -2, \quad b = -3, \quad c = 3
\]

Thus, the value of \( c \) is 3. Looking at the provided options:

1. \( c = -2 \)
2. \( c = 2 \)
3. \( c = 3 \)
4. \( c = -3 \)

The value that is **not** contained in the solution is \( c = 2 \). Therefore, the correct answer is **option 2**.

Would you like any further details or explanations?

Here are five follow-up questions you might find useful:
1. How do you solve systems of equations using substitution?
2. Can systems of equations have more than one solution?
3. How do you check if a system of equations has no solution?
4. What methods can be used to solve systems with more than two variables?
5. How does the determinant relate to solving linear systems?

**Tip**: When solving systems of equations, always check if they are consistent and independent (i.e., have a unique solution) or if they are dependent or inconsistent.

Which value is not contained in the solution of the system shown below?
a + 5b - c = -20
4a - 5b + 4c = 19
-a - 5b - 5c = 2

Determine which value is not part of the solution for a system of three linear equations involving variables a, b, and c. This problem highlights key algebraic concepts, making it suitable for high school students.

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