Confusion on Linear Equation Problem

Question

Given the following problem I understand everything except where $2x_2 = 1 + x_3$ came from, can anyone explain this?

Answer 1

We have the following augmented matrix:

\begin{equation*} A = \begin{pmatrix} 1 & 1 & 1 & 3 \\ 1 & -1 & 2 & 2 \end{pmatrix} \end{equation*}

We applied row reduction by doing the following operation: $-R_2+R_1->R_1$ (this isn't shown in the text)

You will get the following:

\begin{equation*} A = \begin{pmatrix} 0 & 2 & -1 & 1 \\ 1 & -1 & 2 & 2 \end{pmatrix} \end{equation*}

The first row can be read as: $2x_2-x_3=1$ which is equal to $2x_2=1+x_3$