Which statements indicate that an equation has infinitely many solutions? Select all that apply.
a=a
2=2
y=2
x=y

To determine which statements indicate that an equation has infinitely many solutions, we need to understand what it means for an equation to have infinitely many solutions. An equation has infinitely many solutions when it simplifies to a true statement that does not depend on any specific values for the variables involved.

Let's analyze each of the statements:

1. **a = a**  
   This is a true statement for any value of \( a \). It does not impose any restrictions or specific values on \( a \), so it indicates infinitely many solutions.

2. **2 = 2**  
   This is also a true statement. Since it does not involve any variables and is always true, it represents infinitely many solutions.

3. **y = 2**  
   This statement requires \( y \) to equal 2. It does not have infinitely many solutions because only one value for \( y \) (specifically, \( y = 2 \)) satisfies the equation.

4. **x = y**  
   This statement indicates a relationship between \( x \) and \( y \). It can have infinitely many solutions if we consider all possible pairs of values where \( x = y \). However, it is not necessarily always true for any value of \( x \) and \( y \), so it does not by itself indicate infinitely many solutions unless further context specifies that all values are valid.

### Conclusion:
The statements that indicate an equation has infinitely many solutions are:
- **a = a**
- **2 = 2**

### Would you like to explore any other details or have further questions? Here are 5 related questions to expand on this topic:

1. What does it mean when an equation has no solution?
2. Can you give an example of an equation with exactly one solution?
3. How can you tell if a linear system of equations has infinitely many solutions?
4. What is the difference between an identity and a conditional equation?
5. What are some real-world scenarios where equations have infinitely many solutions?

**Tip:** When solving equations, always check if the variables cancel out to reveal a statement like 0 = 0, which indicates infinitely many solutions.

Discover how to identify equations with infinitely many solutions by analyzing true statements such as 'a = a' and '2 = 2'. This algebra problem is suitable for students in Grades 6-8 and focuses on understanding identity equations and infinite solutions.

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