Let the cost of a pencil be $p$ dollars, and the cost of an eraser be $e$ dollars.

From the given information, we can set up the following system of equations:

1. $p + e = 3$ (The cost of a pencil and an eraser is $3.)
2. $3p + 2e = 8$ (The cost of three pencils and two erasers is $8.)

Now, let's solve this system of equations.

Step 1: Solve the first equation for $p$:

$p = 3 - e$

Step 2: Substitute $p = 3 - e$ into the second equation:

$3(3 - e) + 2e = 8$ Simplify: $9 - 3e + 2e = 8$ $9 - e = 8$ $-e = -1$ $e = 1$

Final Answer:

The cost of an eraser is $1.

Would you like a more detailed explanation or have any questions?

Here are some related questions you might find interesting:

1. What would be the cost of 5 pencils and 4 erasers?
2. How would the equations change if the cost of a pencil was doubled?
3. What if we added another condition, like "4 pencils and 3 erasers cost $11"—how would that affect the solution?
4. How can we solve systems of equations with more variables?
5. Can you think of any real-world examples of systems of linear equations like this one?

Tip: When solving systems of equations, substitution or elimination are often useful methods.