To determine what term will make the system equivalent, we first need to analyze the two equations given for System A and System B.
From System A, we have: \[ 7x + 4y = -4 \]
For System B, we have: \[ 5x + 8y = 28 \] and the other equation from System A is also: \[ 7x + 4y = -4 \]
Equivalence of systems means that both systems have the same solutions. We can check if we can manipulate the second equation from System B so that it can relate to the equation in System A.
To find out how to relate these two equations, we can try to express one of the equations in terms of the other.
- Take the equation \( 7x + 4y = -4 \) from System A.
- We need to manipulate the equation from System B, \( 5x + 8y = 28 \).
To convert \( 5x + 8y = 28 \) into a format that relates to \( 7x + 4y = -4 \), we can try to eliminate one of the variables or scale the equations.
To do so, let’s try scaling \( 5x + 8y = 28 \).
However, the relationship may not be directly straightforward. To investigate equivalency, we can try to express one of the equations in terms of the other.
To test if there’s a direct multiplier, we can try multiplying \( 7x + 4y = -4 \) by a certain factor:
If we were to scale \( 7x + 4y = -4 \) by \( -1 \): \[ -7x - 4y = 4 \]
Now, we can try to express the second equation from System B in a similar format:
Let's manipulate the second equation \( 5x + 8y = 28 \): To look for a possible relationship, revert the terms: You can rearrange: \[ 5x + 8y - 28 = 0 \]
From observation, we could multiply this whole equation by an appropriate factor to find the equivalency. However, without a specific factor indicated or choices provided in your original problem statement, we can't conclusively provide a single term that would help make the systems equivalent.
If you provide potential options for the term you are thinking, I can assist you better!
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