To write the augmented matrix for the given system of equations, we first need to rearrange the equations in standard form (Ax + By = C).
The given equations are:
- \( 0 = -y + x \) can be rewritten as \( x - y = 0 \) or \( x - y + 0 = 0 \).
- \( -x + 2y = -2 \) can be rewritten as \( -x + 2y = -2 \).
Now, we can express this system in standard form:
- \( x - y = 0 \)
- \( -x + 2y = -2 \)
Next, we construct the augmented matrix. The coefficients of the variables \( x \) and \( y \) will form the left side of the matrix, and the constants on the right will form the augmented part.
The augmented matrix for this system is:
\[ \begin{bmatrix} 1 & -1 & | & 0 \ -1 & 2 & | & -2 \end{bmatrix} \]
This matrix represents the system of equations, with the vertical line separating the coefficients from the constants.