To solve the system of equations using substitution, we will follow these steps:
1. Solve one of the equations for one variable:
[tex]\[
x - 2 = y
\][/tex]
Solve this for [tex]\( y \)[/tex]:
[tex]\[
y = x - 2
\][/tex]
2. Substitute [tex]\( y = x - 2 \)[/tex] into the second equation:
[tex]\[
-2x + 2y = 2
\][/tex]
Replace [tex]\( y \)[/tex] in the second equation with [tex]\( x - 2 \)[/tex]:
[tex]\[
-2x + 2(x - 2) = 2
\][/tex]
Simplify the equation:
[tex]\[
-2x + 2x - 4 = 2
\][/tex]
The [tex]\( -2x \)[/tex] and [tex]\( 2x \)[/tex] cancel each other out:
[tex]\[
-4 = 2
\][/tex]
This statement is false, which means the system of equations is inconsistent.
Since the system of equations is inconsistent, there are no solutions that satisfy both equations.
Therefore, the answer to the system given is:
[tex]\[
\boxed{\text{No Solution}}
\][/tex]
