To determine which equation will make the systems equivalent, we need to check if the proposed equations are equivalent to the second equation in System A (which is the same as the first in System B).
Given:
- System A: \(3x + 2y = -9\)
- System B: \(5x - 3y = 4\)
We need to check each response option by seeing if each proposed equation can be simplified (or manipulated) to yield one of the original equations.
Option 1: \(6x + 4y = 18\)
This can be simplified by dividing everything by 2: \[ 3x + 2y = 9 \] This is not equivalent to \(3x + 2y = -9\) or \(5x - 3y = 4\).
Option 2: \(-1x + 8y = -5\)
Rearranging, \[ x - 8y = 5 \] or \[ x = 8y + 5 \] This does not match either of the original equations.
Option 3: \(8x - y = 5\)
Rearranging gives: \[ y = 8x - 5 \] This does not match either of the original equations.
Option 4: \(8x - y = -5\)
Rearranging gives: \[ y = 8x + 5 \] This does not match either of the original equations.
Conclusion:
After evaluating each option, we realize that none of the proposed equations provided were found to be equivalent to \(5x - 3y = 4\) or \(3x + 2y = -9\) directly through simplification or substitution.
However, since it's common in the context of creating equivalent systems to multiply one of the given equations, let's examine the original equations as they relate. The equation \(5x - 3y = 4\) can have multiple equivalents by scaling it up or down.
It appears none of the presented options make either system equivalent through direct substitution. Without additional context for these specific equations, the terms provided may not yield the necessary equivalence directly.
Would you require further assistance with a different query or provide clarity on any missed area?