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The system of equations provided is:

\[
\begin{aligned}
2x + 5y &= 18 \\
8x + 20y &= 72
\end{aligned}
\]

We will use the **method of elimination** to solve the system.

### Step 1: Simplify the second equation (if possible)
Notice that the second equation can be simplified. Divide the entire second equation by 4:

\[
\frac{8x + 20y}{4} = \frac{72}{4} \implies 2x + 5y = 18
\]

Thus, both equations are actually the same:

\[
2x + 5y = 18
\]

### Step 2: Determine the type of system
Since the two equations are identical, we have a **dependent system**, meaning there are infinitely many solutions. The solution set will depend on one of the variables.

### Step 3: Express the solution
Since the system is dependent, we can express one variable in terms of the other. Using the first equation \( 2x + 5y = 18 \), solve for \( x \) in terms of \( y \):

\[
x = \frac{18 - 5y}{2}
\]

Thus, the general solution is:

\[
(x, y) = \left( \frac{18 - 5y}{2}, y \right)
\]

### Conclusion:
The system is **dependent**, and the solution set is \( \left( \frac{18 - 5y}{2}, y \right) \), where \( y \) is any real number.

Would you like more details on this method or how to handle such systems? Here are some related questions:

1. How can you tell if a system of equations is dependent?
2. What are the key differences between dependent and inconsistent systems?
3. How do you approach solving systems using substitution versus elimination?
4. In what scenarios would a system have only one solution?
5. What is the geometric interpretation of a dependent system of linear equations?

**Tip:** Always check if equations can be simplified before applying elimination to save time.

Use the method of elimination to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form. The system of equations is:
2x + 5y = 18
8x + 20y = 72

Learn how to solve the system of linear equations 2x + 5y = 18 and 8x + 20y = 72 using the elimination method. This problem demonstrates the concept of dependent systems, showing how to express one variable in terms of the other. Suitable for students in Grades 9-12.

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