To solve the system of equations:

1. $4x + 2y = 16$
2. $x + 2y = 16$

Step 1: Eliminate one variable

We can subtract the second equation from the first to eliminate $y$:

$(4x + 2y) - (x + 2y) = 16 - 16$

$3x = 0$

$x = 0$

Step 2: Substitute $x = 0$ into the second equation

Substituting $x = 0$ into $x + 2y = 16$:

$0 + 2y = 16$

$2y = 16 \quad \Rightarrow \quad y = 8$

Solution:

The solution to the system is: $x = 0, \; y = 8$

Verification:

1. Substitute $x = 0, y = 8$ into $4x + 2y = 16$: $4(0) + 2(8) = 16 \quad \text{True.}$

2. Substitute $x = 0, y = 8$ into $x + 2y = 16$: $0 + 2(8) = 16 \quad \text{True.}$

Final Answer:

$(x, y) = (0, 8)$

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Would you like a more detailed explanation or help with graphing?

Here are some related questions to explore:

1. How do you graph this system of equations?
2. What does elimination mean in solving systems of equations?
3. Can this system have any other solutions?
4. How do we solve systems using substitution instead of elimination?
5. What is the geometrical interpretation of the solution?

Tip: Always verify your solution by substituting it back into the original equations!