To solve the given system of equations:
1. [tex]\( x + 2y - z = 8 \)[/tex]
2. [tex]\( x + y - 2x = 0 \)[/tex]
Let's solve it step by step:
### Step 1: Simplify the Second Equation
First, take the second equation:
[tex]\[ x + y - 2x = 0 \][/tex]
Combine like terms:
[tex]\[ -x + y = 0 \][/tex]
This simplifies to:
[tex]\[ y = x \][/tex]
### Step 2: Substitute [tex]\( y = x \)[/tex] into the First Equation
Now substitute [tex]\( y = x \)[/tex] into the first equation:
[tex]\[ x + 2y - z = 8 \][/tex]
Substitute [tex]\( y \)[/tex] with [tex]\( x \)[/tex]:
[tex]\[ x + 2(x) - z = 8 \][/tex]
Simplify the terms:
[tex]\[ x + 2x - z = 8 \][/tex]
[tex]\[ 3x - z = 8 \][/tex]
### Step 3: Solve for [tex]\( z \)[/tex] in terms of [tex]\( x \)[/tex]
From the equation [tex]\( 3x - z = 8 \)[/tex], isolate [tex]\( z \)[/tex]:
[tex]\[ z = 3x - 8 \][/tex]
### Solution
The system of equations is now simplified to:
[tex]\[ y = x \][/tex]
[tex]\[ z = 3x - 8 \][/tex]
Thus, the simplified system is:
[tex]\[ y = x \][/tex]
[tex]\[ z = 3x - 8 \][/tex]
