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Let's solve the given system of linear equations using the substitution method:

### Given System of Equations
1) \( y = 2x + 9 \)
2) \(-4x + 2y = 1\)

### Step 1: Substituting \( y \) from Equation (1) into Equation (2)
Since \( y = 2x + 9 \), we substitute this into the second equation:

\[
-4x + 2(2x + 9) = 1
\]

### Step 2: Simplify the equation
\[
-4x + 4x + 18 = 1
\]
\[
18 = 1
\]

This is a contradiction, meaning the system of equations is inconsistent. Therefore, there is **no solution** to this system.

The correct answer is **"DNE" (Does Not Exist)** for both blanks as specified.

Would you like any further details or explanations? Here are some follow-up questions for practice:

1. How do you identify if a system is inconsistent without solving it?
2. What are the different types of solutions a system of linear equations can have?
3. Can the substitution method always be used, or are there situations where another method is preferred?
4. What does it mean geometrically for a system of equations to have no solution?
5. How can you determine if two equations represent the same line?

**Tip:** Always simplify the equations fully when using substitution to avoid missing contradictions.

Solve the following system of equations using the substitution method:
1) y = 2x + 9
2) -4x + 2y = 1

Learn how to solve a system of linear equations using the substitution method with a detailed step-by-step explanation. The example highlights an inconsistent system with no solution. Suitable for students in Grades 9-11.

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