To solve the system of equations given:

1. Equations:

   • $2x + y = 18$
   • $y = 4x$

2. Substitution Method: Substitute $y = 4x$ from the second equation into the first equation:

   $2x + (4x) = 18$

   Combine like terms:

   $6x = 18$

   Solve for $x$:

   $x = 3$

3. Find $y$: Substitute $x = 3$ into $y = 4x$:

   $y = 4(3) = 12$

4. Solution: The system has a single solution, which is:

   $(x, y) = (3, 12)$

The correct answer is A: The system has a single solution. The solution set is $(3, 12)$.

Do you want further explanation or have any questions about this solution?

Related Questions:

1. What are dependent equations, and how do you identify them?
2. How can substitution and elimination methods be compared?
3. What makes a system of equations inconsistent?
4. Can you explain how to graphically interpret this solution?
5. How can you verify a solution in a system of linear equations?

Tip: Always substitute the solution back into both equations to ensure accuracy!