To find the intersection of the two lines given by the equations \( y = -x + 4 \) and \( y = 2x - 2 \), we can set the two equations equal to each other:
\[ -x + 4 = 2x - 2 \]
Now, we'll solve for \( x \):
- Add \( x \) to both sides:
\[ 4 = 3x - 2 \]
- Add \( 2 \) to both sides:
\[ 6 = 3x \]
- Divide by \( 3 \):
\[ x = 2 \]
Now that we have \( x \), we can substitute it back into either of the original equations to find \( y \). We'll use the first equation:
\[ y = -x + 4 = -2 + 4 = 2 \]
So, the intersection point of the two lines is:
\[ (x, y) = (2, 2) \]
Thus, the solution is \( (2, 2) \).