To solve the system of equations given by [tex]\( y = 4x - 8 \)[/tex] and [tex]\( y = 4x + 2 \)[/tex], we need to determine if there is a point [tex]\((x, y)\)[/tex] that satisfies both equations simultaneously.
1. Set the equations equal to each other:
Since both equations are equal to [tex]\( y \)[/tex], we can set them equal to each other:
[tex]\[
4x - 8 = 4x + 2
\][/tex]
2. Simplify the equation:
To find the value of [tex]\( x \)[/tex], we aim to isolate [tex]\( x \)[/tex]. Let's subtract [tex]\( 4x \)[/tex] from both sides of the equation:
[tex]\[
4x - 4x - 8 = 4x - 4x + 2
\][/tex]
Simplifying both sides, we get:
[tex]\[
-8 = 2
\][/tex]
3. Analyze the result:
The equation [tex]\( -8 = 2 \)[/tex] is a contradiction, meaning it is not true. This indicates that there is no value of [tex]\( x \)[/tex] that will satisfy both equations simultaneously.
Since the simplified result led to a contradiction, there is no solution where both equations intersect.
Therefore, the correct answer is:
[tex]\[
\boxed{\text{None of the above}}
\][/tex]
