Let's go through the questions and their solutions one by one.

1. What is the substitution equation?

You are given two equations:

1. $2x + 4y = 8$
2. $x = 2$

The substitution equation comes from substituting $x = 2$ into the first equation: $2(2) + 4y = 8$ This is the substitution equation: $4 + 4y = 8$

2. What is the nickname of the variable?

The variable being substituted is $x$. The "nickname" for $x$ could simply be "the known value" or "the replaced variable."

3. Who does the nickname rename?

The nickname "the known value" or "the replaced variable" renames the variable $x$, because it's the value that you are replacing in the equation.

4. Where should the substitution be made (which equation) 1 or 2?

The substitution should be made in equation 1, because equation 2 already gives the value of $x$. You need to substitute this value into equation 1.

5. What is the solution as an ordered pair?

After substituting $x = 2$ into the first equation, you get: $4 + 4y = 8$ Solve for $y$: $4y = 8 - 4$ $4y = 4$ $y = 1$ So, the solution as an ordered pair is $(x, y) = (2, 1)$.

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Would you like further details on any part of this process?

Here are 5 related questions for deeper understanding:

1. How do you solve the equation $4 + 4y = 8$ step by step?
2. Why is it important to substitute the value of $x$ into equation 1?
3. What would happen if the value of $x$ were different in equation 2?
4. How can you verify that the solution $(2, 1)$ is correct?
5. What do the variables $x$ and $y$ represent in this context?

Tip: Substitution is a powerful method for solving systems of equations. Always check your solution by substituting it back into the original equations to ensure accuracy.