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.