To determine which of the given options can make System B equivalent to System A, we first recognize that two systems of equations are equivalent if one equation can be obtained from the other through multiplication or addition/subtraction of equations.
The first equation in both systems is \(7x + 4y = -4\). We need to find an equivalent second equation for System B based on the second equation in System A, which is \(5x + 8y = 28\).
We can manipulate this second equation to see if one of the options represents the same line.
- Start with the equation \(5x + 8y = 28\).
- We can multiply the entire equation by any non-zero constant to generate equivalent equations.
Let’s analyze each option to see if it can be simplified to \(5x + 8y = 28\).
Option A: \(12x + 12y = 24\)
Dividing through by 12 gives \(x + y = 2\). This is not equivalent to \(5x + 8y = 28\).
Option B: \(-14 - 8y = -8\)
Rearranging gives \(-8y = 6\), or \(y = -\frac{3}{4}\). This is not an equation in terms of \(x\) and \(y\) in the form that we can compare.
Option C: \(-14x - 8y = 8\)
Multiply the entire equation by -1 to get: \[ 14x + 8y = -8. \] This can be rearranged to: \[ 5x + 8y = 28 \quad \text{(not equivalent)}\]
Option D: \(-12x - 12y = 24\)
Dividing through by -12 gives: \[ x + y = -2. \] Again, this is not equivalent to \(5x + 8y = 28\).
Since none of the options seem to correctly represent the manipulated second equation from System A, we must check if any of the proposed options can actually be transformed into \((5x + 8y = 28)\).
Upon careful review, it seems that no option can yield an equivalent form of \(5x + 8y = 28\).
Final conclusion: none of the options A, B, C, or D make System B equivalent to System A.
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