To determine which equations make the systems equivalent, we need to find a way to transform the given equations in System A into the corresponding equation in System B.
Given:
- System A: \( 7x + 4y = -4 \)
- System B: \( 5x + 8y = 28 \)
We need to manipulate the equations to see which of the options could turn into one of these equations.
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Option 1: \(-12x - 12y = 24\)
- This equation can be simplified: multiplying it by -1 gives \(12x + 12y = -24\).
- This does not match any form of equations A or B.
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Option 2: \(-14x - 8y = -8\)
- Rearranging gives \(14x + 8y = 8\).
- This does not match.
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Option 3: \(12x + 12y = 24\)
- Simplified: \(12x + 12y = 24\), simplifies to \(x + y = 2\) or other values.
- This does not match.
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Option 4: \(-14x - 8y = 8\)
- Rearranging gives \(14x + 8y = -8\).
- This does not simplify to match any form of equations A or B.
Conclusion: None of the provided choices directly transform to show equivalence with System A or System B. However, let's conduct a more thorough check and see if the second option might provide consistency with a different manipulation or identify potential errors in others.
The point of finding equivalency is to discover if scaling and translating via operations gives us similar lines.
In this exhaustive check:
- Take \(7x + 4y = -4\), where scaling by patterns results equivalently toward later reformulated outputs.
- At least one of the equations should eventually yield a way to rearrange toward B via similarities (coefficients remaining consistent).
Moral: Upon reviewing patterns, none yield congruence directly, suggesting there might need to inspect for potential variations beyond indicated forms in connection to linearity and parallelism—however, one might closely visualize \(−14x - 8y = 8\) as having alignment initially targeting the resultant forms.
The most congruent provision to the given might solely rely on academic scrutiny reflecting perspective rather than a direct match.
In conclusion, the best responding equation aiming for the resultant similarity might likely leave ambiguity not distinctly refining an equivalent which hints you are likely to reformulate or restructure entirely divergent systems needing intervention to align under your taught system equivalence provided.
For accurate options here, \(−14x−8y=8\) relates most closely in linear relationship checks indicative but pushes to n-factor outlines.
So:
The most relevant problem-solving context here could suggest closely influential on ignoring standard assumptions leading toward transformative output meaning-direct equivalencies in checks systematically today.
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