To determine the number of solutions for the system of equations given:
- \( 8x - 6y = 48 \)
- \( 8x + 6y = 48 \)
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
1 answer