To determine which equation will make System B equivalent to System A, we first need to manipulate the equation from System A to see what form it takes.
We have:
- System A: \[ 7x + 4y = -4 \]
We should check the second equation in System B to see how it relates to System A.
- System B: \[ 5x + 8y = 28 \]
Now we can manipulate the equation from System B to see if we can find a relationship to the first equation from System A.
We can put both equations in a similar standard form \(Ax + By = C\) to see if they're equivalent:
- Multiply System A equation by a scalar if needed, to reach similar coefficients with System B.
- Rearrange System B equation: Multiply the first equation \(7x + 4y = -4\) by 2 to match the variables better.
Multiplying: \[ 2(7x + 4y) = 2(-4) \implies 14x + 8y = -8 \]
Now, we have:
- Transformed System A: \[ 14x + 8y = -8 \]
Now we look at all the given choices to find which is equal to \(14x + 8y = -8\) after suitable manipulation:
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Check the first option: \[ -12x - 12y = 24 \] Rewriting this: \[ 12x + 12y = -24 \quad \text{(not equivalent)} \]
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Check the second option: \[ -14x - 8y = 8 \] Rewriting this: Multiplying by \(-1\): \[ 14x + 8y = -8 \quad \text{(equivalent)} \]
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Check the third option: \[ 12x + 12y = 24 \] (not equivalent)
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Check the fourth option: \[ -14x - 8y = -8 \] Rewriting this: Multiplying by \(-1\): \[ 14x + 8y = 8 \quad \text{(not equivalent)} \]
The only choice that is equivalent or can be manipulated to match \[14x + 8y = -8\] is:
\[ \boxed{-14x - 8y = 8} \]