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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.

(4, 2) is a solution to the system of equations below:
2x + 4y = 16
(1/2)x - 2y = 4
Select one: True or False

Check if the point (4, 2) satisfies the system of equations 2x + 4y = 16 and (1/2)x - 2y = 4. Learn how to substitute values into both equations and verify the solution step-by-step. Suitable for students in Grades 8-10.

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