We have a system of three equations with three variables:

\[
1. \, 7x - 5y + 6z = -3
\]
\[
2. \, -3x - 6y = -7
\]
\[
3. \, 4x - y - 2z = -5
\]

### Step 1: Simplify and rearrange equations (if needed)
The second equation can be rewritten to isolate \( y \):

\[
-3x - 6y = -7 \quad \Rightarrow \quad y = \frac{-3x + 7}{6}
\]

### Step 2: Substitution
Substitute \( y \) into the first and third equations.

Would you like to proceed with the substitution, or prefer a different method (e.g., elimination or matrix solution)?

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Would you like further details or have any questions?  
Here are 5 related questions for deeper understanding:
1. How would you solve this system using the substitution method?
2. Can you eliminate one variable from these equations?
3. What happens if you convert this system into a matrix and use row reduction?
4. Could you apply Cramer's Rule to this system?
5. How can you check if the system has a unique solution?

**Tip:** When solving systems of equations, try simplifying one of the equations first.

7x - 5y + 6z = -3, -3x - 6y = -7, 4x - y - 2z = -5

Learn how to solve a system of three equations with three variables using the substitution method. This detailed solution includes step-by-step substitution and manipulation of the linear equations 7x - 5y + 6z = -3, -3x - 6y = -7, and 4x - y - 2z = -5. Ideal for students in Grades 10-12.

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