Solving with Elimination Quick Check

To determine the number of solutions for the system of equations given:

1. \( 8x - 6y = 48 \)
2. \( 8x + 6y = 48 \)

Let's analyze the equations. We can begin by subtracting the first equation from the second:

\[
(8x + 6y) - (8x - 6y) = 48 - 48
\]

This simplifies to:

\[
12y = 0
\]

From here, we can solve for \( y \):

\[
y = 0
\]

Now, substitute \( y = 0 \) back into one of the original equations to find \( x \). We'll use the first equation:

\[
8x - 6(0) = 48
\]

This simplifies to:

\[
8x = 48
\]

Now, solving for \( x \):

\[
x = 6
\]

Thus, we have found a unique solution: \( (x, y) = (6, 0) \).

From this analysis, we can conclude that the system of equations has **one solution**.

So the correct response is:

**one**