To find the solution to the given system of equations step-by-step, we need to simplify each equation individually. Let's break it down:
Given system of equations:
[tex]\[
\left\{
\begin{array}{l}
x + 2 + z \\
5 + y + z \\
2 + 3 - z
\end{array}
\right.
\][/tex]
### Equation 1:
[tex]\[ x + 2 + z \][/tex]
This equation is already in its simplest form. So, it remains:
[tex]\[ x + z + 2 \][/tex]
### Equation 2:
[tex]\[ 5 + y + z \][/tex]
To simplify this equation, let's combine the constants:
[tex]\[ 5 + y + z - 5 \][/tex]
Here, the constants 5 and -5 add up to 0:
So, the simplified form is:
[tex]\[ y + z \][/tex]
### Equation 3:
[tex]\[ 2 + 3 - z \][/tex]
First, let's combine the constants (2 and 3):
[tex]\[ 2 + 3 - z = 5 - z \][/tex]
After simplification, the equation is:
[tex]\[ 5 - z \][/tex]
Thus, the simplified system of equations is:
[tex]\[
\left\{
\begin{array}{l}
x + z + 2 \\
y + z \\
5 - z
\end{array}
\right.
\][/tex]
This is the final, simplified form of the given system of equations.
