Complete the statement to describe the solution to the following system of equations.
 
	15x−5y=20
6x−2y=8

This system of equations has (Select) 

Let's solve the system of equations:

The system is:
\[
\begin{aligned}
15x - 5y &= 20 \quad \text{(Equation 1)} \\
6x - 2y &= 8 \quad \text{(Equation 2)}
\end{aligned}
\]

### Step 1: Simplify both equations
We can simplify both equations to make them easier to compare or solve.

- Divide Equation 1 by 5:
\[
\frac{15x - 5y}{5} = \frac{20}{5} \quad \Rightarrow \quad 3x - y = 4
\]

- Divide Equation 2 by 2:
\[
\frac{6x - 2y}{2} = \frac{8}{2} \quad \Rightarrow \quad 3x - y = 4
\]

### Step 2: Compare the equations
Both simplified equations are identical:
\[
3x - y = 4
\]

This means the two equations represent the **same line**. As a result, every point that lies on this line is a solution to the system.

### Conclusion:
The system of equations has **infinitely many solutions**, because the two equations describe the same line.

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Would you like more details on solving systems of equations or any other questions about this process? Here are some related questions for deeper understanding:

1. What is the graphical interpretation of two identical equations in a system?
2. How do you identify whether a system of equations has no solution, one solution, or infinitely many solutions?
3. What are the methods for solving systems of equations (e.g., substitution, elimination)?
4. How can you tell if a system of equations is consistent or inconsistent?
5. How can systems of linear equations be applied to real-world problems?

**Tip:** Always simplify equations when possible, as it can make the system easier to solve or interpret!

Complete the statement to describe the solution to the following system of equations: 15x−5y=20 and 6x−2y=8. This system of equations has (Select).

This guide shows how to solve the system of linear equations 15x−5y=20 and 6x−2y=8. Learn how to simplify equations and understand the concept of infinitely many solutions. Suitable for students in Grades 9-10 studying algebra.

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