2x+4y=8

x=2

What is the substitution equation? 
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What is the nickname of the variable? 
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Who does the nickname rename? 
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Where should the substitution be made(which equation) 1 or 2?  
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What is the solution as an ordered pair? 
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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 \( (x, y) = (2, 1) \).

---

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.

2x+4y=8
x=2
What is the substitution equation?
What is the nickname of the variable?
Who does the nickname rename?
Where should the substitution be made(which equation) 1 or 2?
What is the solution as an ordered pair?

Learn how to solve the system of linear equations 2x + 4y = 8 and x = 2 using the substitution method. This example demonstrates key algebraic techniques, perfect for students in Grades 8-10.

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