https://file.aiquickdraw.com/mathbot/file/1727820887405tsm1rsrx.jpg

The system of equations given in the image is:

\[
\begin{aligned}
1. & \ -3a + b - 4c = 21 \\
2. & \ 6a + 6b = -6 \\
3. & \ 3a + 4b - c = -7
\end{aligned}
\]

Let's solve this system step-by-step using the method of substitution or elimination.

### Step 1: Simplify equation 2
We can simplify the second equation by dividing everything by 6:

\[
a + b = -1
\]
This simplifies to:

\[
a = -1 - b
\]

### Step 2: Substitute \(a = -1 - b\) into equation 1 and equation 3

#### Substitution into equation 1:
\[
-3(-1 - b) + b - 4c = 21
\]
Simplifying:
\[
3 + 3b + b - 4c = 21
\]
\[
4b - 4c = 18 \quad \text{(subtracting 3 from both sides)}
\]
\[
b - c = 4.5
\]

#### Substitution into equation 3:
\[
3(-1 - b) + 4b - c = -7
\]
Simplifying:
\[
-3 - 3b + 4b - c = -7
\]
\[
b - c = -4
\]

### Step 3: Solve for \(b\) and \(c\)
We now have two equations:
1. \(b - c = 4.5\)
2. \(b - c = -4\)

This setup seems inconsistent, suggesting there might be a mistake in either the interpretation of the constants or the equations. Would you like to recheck the constants or approach this differently?

Please let me know if you want further details or have questions. 

Here are some relevant questions:
1. Would you like me to verify any step in particular?
2. Do you prefer solving this using another method (e.g., matrix or graphing)?
3. Should I double-check the second equation for simplification?
4. Are there any other equations from the problem not visible in the image?
5. Would you like more context on handling systems of linear equations?

**Tip:** When solving systems of equations, it's often helpful to reduce equations to simpler forms for easier substitution or elimination.

Solve the system of equations:
1. -3a + b - 4c = 21
2. 6a + 6b = -6
3. 3a + 4b - c = -7

Step-by-step solution of a system of three linear equations: -3a + b - 4c = 21, 6a + 6b = -6, and 3a + 4b - c = -7. The solution involves using substitution and elimination methods. This problem is suitable for high school students in Grades 9-12.

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