Write the system of equations associated with the augmented matrix. Do not solve.
[tex]\[
\left[\begin{array}{lll|l}
1 & 0 & 0 & 2 \\
0 & 1 & 0 & 5 \\
0 & 0 & 1 & 1
\end{array}\right]
\][/tex]
Complete the system shown below. Use the letters \( x \), \( y \), and \( z \) to represent the terms from the first, second, and third columns of the matrix, respectively.
[tex]\[
\begin{cases}
x & = 2 \\
y & = 5 \\
z & = 1
\end{cases}
\][/tex]
(Simplify your answer.)