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.
