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**