To determine which statement is true regarding the values \( x = -5 \) and \( y = 0.25 \), we must first modify equation \( A \) and then analyze equation \( B \) based on the information provided.
Step 1: Rewrite Equation A
The equation \( A \) is given as: \[ 4y - 3x = 16 \]
We can rearrange it to express \( y \) in terms of \( x \): \[ 4y = 3x + 16 \] \[ y = \frac{3}{4}x + 4 \]
Step 2: Substitute the Intersection Point into Equation A
Now, substitute \( x = -5 \) and \( y = 0.25 \) into equation \( A \): \[ 4(0.25) - 3(-5) = 16 \] Calculating each part: \[ 1 - (-15) = 16 \] \[ 1 + 15 = 16 \] This is true. Thus, the point \( (-5, 0.25) \) satisfies equation \( A \).
Step 3: Analyze Equation B
We do not have the explicit form of equation \( B \) as presented. However, Antonio found the lines to intersect at that single point, which suggests that equation \( B \) must also incorporate that point.
Step 4: Conclusion
Since the x and y values \( (-5, 0.25) \) satisfy equation \( A \) and the problem states they intersect at that point, it implies that they also satisfy equation \( B \). Hence:
The correct option is: C. They are the only values that make both equations true.
This means that the intersection point also communicates that the two equations are distinct lines that meet only at this point.