To solve the system of equations given by:
- \( y = 2x + 4 \) (Equation 1)
- \( -2x + y = 8 \) (Equation 2)
We can substitute Equation 1 into Equation 2.
Substituting \( y \) in Equation 2:
\[ -2x + (2x + 4) = 8 \]
Now simplify this equation:
\[ -2x + 2x + 4 = 8 \]
The \( -2x \) and \( 2x \) cancel each other out:
\[ 4 = 8 \]
This statement is false, which suggests that the system of equations has no solution. The lines represented by these equations are parallel and do not intersect.
Thus, the solution to this system is that there are no points \((x, y)\) that satisfy both equations simultaneously.