To determine which of the given equations will make the systems equivalent, we need to analyze the first equation of System A and the second equation of System B.
The first equation from System A is: \[ 7x + 4y = -4 \]
To find an equivalent equation for System B, we can multiply the entire equation by a constant. In this case, we'll consider multiplying the first equation by -2 to verify the equivalency.
If we multiply by -2: \[ -2(7x + 4y) = -2(-4) \] This simplifies to: \[ -14x - 8y = 8 \]
Now, we compare this derived equation to the options given. The option that matches is: \[ -14x - 8y = 8 \]
Now, let’s check if any of the other options can also yield the same results.
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Option: 12x + 12y = 24
- This doesn't seem related to the first equation.
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Option: −12x − 12y = 24
- This doesn't seem related to the first equation.
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Option: −14x − 8y = −8
- This can be obtained by multiplying the original equation \( 7x + 4y = -4 \) by -2, but it results in a different constant on the right-hand side compared to our derived equation.
Therefore, the correct response that will create an equivalent system is: −14x − 8y = 8.