To determine the number of solutions for the system of equations:
- \(8x - 6y = 48\) (Equation 1)
- \(8x + 6y = 48\) (Equation 2)
Let's solve the equations.
First, we can rewrite both equations in standard form:
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From Equation 1: \[ 8x - 6y = 48 \quad \text{(Equation 1)} \]
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From Equation 2: \[ 8x + 6y = 48 \quad \text{(Equation 2)} \]
Next, we can try to eliminate \(x\) by subtracting one equation from the other:
\[ (8x - 6y) - (8x + 6y) = 48 - 48 \] This simplifies to: \[ -12y = 0 \]
Dividing both sides by -12 gives: \[ y = 0 \]
Now, substituting \(y = 0\) back into either of the original equations to find \(x\). Let's use Equation 1:
\[ 8x - 6(0) = 48 \] This simplifies to: \[ 8x = 48 \] Dividing by 8 gives: \[ x = 6 \]
Thus, there is a single solution to the system, which is the point \((6, 0)\).
Conclusion: The system of equations has one solution. The correct response is "one."