We are asked to check if the point $(4, 2)$ is a solution to the system of equations:

$\text{1st equation: } 2x + 4y = 16$ $\text{2nd equation: } \left( \frac{1}{2} \right) x - 2y = 4$

We substitute $x = 4$ and $y = 2$ into both equations to verify.

1st Equation:

Substitute $x = 4$ and $y = 2$ into the first equation:

$2(4) + 4(2) = 16$ $8 + 8 = 16$ $16 = 16$ This is true.

2nd Equation:

Substitute $x = 4$ and $y = 2$ into the second equation:

$\left( \frac{1}{2} \right)(4) - 2(2) = 4$ $2 - 4 = 4$ $-2 = 4$ This is false.

Since the second equation is not satisfied, the point $(4, 2)$ is not a solution to the system of equations. Therefore, the correct answer is:

False.

Would you like more details or have any questions?

Here are five related questions to explore further:

1. What is the method to solve systems of equations using substitution?
2. Can a system of equations have no solution? Why?
3. How does the graphical method help in solving systems of equations?
4. What is the importance of checking both equations when verifying a solution?
5. Can a point satisfy one equation but not the other in a system?

Tip: When verifying solutions to systems of equations, always check each equation independently to ensure consistency.