Given the following system of equations: -4x + 8 = 16 and 2x + 4y = 32, to create the new equivalent system of equations -2x + 4y = 8 and 2x + 4y = 32, the first equation was divided by -2.

To understand how we obtain the new system of equations from the given system, let's analyze the transformation step by step.

The given system of equations is: 1) -4x + 8 = 16 2) 2x + 4y = 32

The problem states that the first equation was divided by -2 to create an equivalent equation. Dividing each term in the first equation by -2 will result in: (-4x / -2) + (8 / -2) = (16 / -2)

Simplifying each term gives us: 2x - 4 = -8

But we wanted the new equation to be -2x + 4y = 8, according to what was stated. There seems to be a mistake either in the transformation process or in the statement of the new system because when we divide the first original equation by -2, we do not get -2x + 4y = 8.

Let's check by correcting what appears to be the transcription error and divide the entire first equation by -2: (-4x / -2) + (8 / -2) = (16 / -2)

Calculating each part: 2x - 4 = -8

To get to the correct form as mentioned (-2x + 4y = 8), we can multiply the entire equation we got from the division by -1: (2x - 4) * -1 = (-8) * -1

This gives us: -2x + 4 = 8

Now, we are still missing the "y" term. Since the original equation does not have a "y" term, there is no way to just divide or multiply to get a "y" term from the first original equation. It seems there is a misunderstanding in the statement provided.

The new system of equation provided (-2x + 4y = 8 and 2x + 4y = 32) cannot be obtained by merely dividing the first original equation by -2. The "4y" term appears to be mistakenly inserted into the equation, or there may have been an error in how the problem was conveyed.