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To solve this system of equations for \( x \), \( y \), and \( z \), let's start by writing down the equations:

1. \( 8x + y + 4z = 9 \)
2. \( 4x - 3y + z = 7 \)
3. \( 8x - 4y + 5z = -2 \)

### Step 1: Eliminate one variable
Let's eliminate \( x \) by combining equations.

1. **Subtract Equation 1 from Equation 3**:
   \[
   (8x - 4y + 5z) - (8x + y + 4z) = -2 - 9
   \]
   This simplifies to:
   \[
   -5y + z = -11 \quad \Rightarrow \quad z = -11 + 5y
   \]

2. **Combine Equations 1 and 2**:
  

Solve the following system of equations for all three variables.

8x + y + 4z = 9
4x - 3y + z = 7
8x - 4y + 5z = -2

Learn how to solve a system of three linear equations involving variables x, y, and z with a detailed step-by-step solution. This problem covers key algebraic concepts, including elimination and substitution methods. Suitable for high school students in Grades 9-12.

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