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Solve the system of equations:
[tex]\[ \left\{\begin{array}{l} x + 2y - z = 8 \\ x + y - 2z = 6 \end{array}\right. \][/tex]

Sagot :

GinnyAnswer
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]
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