To determine if $(2, 4)$ is a solution to the system of equations:

1. The system of equations is: $y = 6x - 8$ $y = 3x + 2$

2. Substitute $x = 2$ and $y = 4$ into both equations and check if both hold true.

First equation:
$y = 6x - 8$
Substitute $x = 2$ and $y = 4$:
$4 = 6(2) - 8 \implies 4 = 12 - 8 \implies 4 = 4$
This is true.

Second equation:
$y = 3x + 2$
Substitute $x = 2$ and $y = 4$:
$4 = 3(2) + 2 \implies 4 = 6 + 2 \implies 4 = 8$
This is false.

Since $(2, 4)$ satisfies the first equation but not the second, it is not a solution to the system of equations.

Answer: No.

Would you like more details or have any questions? Here are some related questions to deepen understanding:

1. How do you verify solutions for a system of equations graphically?
2. What does it mean geometrically if one equation is satisfied and the other is not?
3. How can you solve this system algebraically to find the intersection point?
4. What is the general definition of a solution to a system of linear equations?
5. How can substitution or elimination methods help solve such systems?

Tip: Always check solutions in both equations when verifying for a system.