To determine whether the system of equations is consistent and independent, consistent and dependent, or inconsistent, let's analyze the given equations step by step:
1. The first equation is:
[tex]\[
y = -x + 1
\][/tex]
2. The second equation is:
[tex]\[
2y = -2x + 2
\][/tex]
First, we can simplify the second equation by dividing every term by 2:
[tex]\[
\frac{2y}{2} = \frac{-2x + 2}{2}
\][/tex]
[tex]\[
y = -x + 1
\][/tex]
This simplified second equation, [tex]\( y = -x + 1 \)[/tex], is identical to the first equation.
When both equations are the same, we have what is known as a dependent system. This means that the equations represent the same line, and there are infinitely many solutions (every point on the line satisfies both equations).
Therefore, the system is consistent and dependent.
So, the correct answer is:
[tex]\[
\boxed{2}
\][/tex]
