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) 

We are given the following system of equations:

1. \( 15x - 5y = 20 \)
2. \( 6x - 2y = 8 \)

Let's solve this system step-by-step to determine the nature of the solution:

### Step 1: Simplify the equations

Both equations can be simplified by dividing them by common factors:

- Divide the first equation by 5:  
  \( \frac{15x - 5y}{5} = \frac{20}{5} \)  
  This simplifies to:  
  \( 3x - y = 4 \)

- Divide the second equation by 2:  
  \( \frac{6x - 2y}{2} = \frac{8}{2} \)  
  This simplifies to:  
  \( 3x - y = 4 \)

### Step 2: Compare the equations

Now we have:

1. \( 3x - y = 4 \)
2. \( 3x - y = 4 \)

These two equations are identical, meaning they represent the same line. When two equations are identical, the system has **infinitely many solutions**, because every point on the line is a solution.

### Conclusion:
The system of equations has **infinitely many solutions**.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. What are the possible types of solutions for a system of linear equations?
2. How do you solve systems of equations using substitution or elimination methods?
3. What does it mean when two lines are parallel but not identical in a system of equations?
4. How can graphing help visualize the solutions of a system of linear equations?
5. What are some examples of systems with no solution?

**Tip**: If two equations simplify to the same equation, they represent the same line, leading to infinitely many solutions.

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)

Learn how to solve the system of equations 15x−5y=20 and 6x−2y=8 step-by-step. Simplify the equations and understand why they have infinitely many solutions. Suitable for students in Grades 8-10, covering core algebraic concepts and methods for solving systems of equations.

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