To create the new equivalent system of equations:
[tex]$
\begin{array}{l}
-2x + 4y = 8 \\
2x + 4y = 32
\end{array}
$[/tex]
from the original system of equations:
[tex]$
\begin{array}{l}
-4x + 8y = 16 \\
2x + 4y = 32
\end{array}
$[/tex]
we need to determine what transformation was applied.
The transformation done was:
Divide the first equation, [tex]\(-4x + 8y = 16\)[/tex], by 2.
By performing this division, the first equation changes as follows:
[tex]\(-4x + 8y = 16 \)[/tex]
Dividing each term by 2:
[tex]\(\frac{-4x}{2} + \frac{8y}{2} = \frac{16}{2} \)[/tex]
results in:
[tex]\(-2x + 4y = 8\)[/tex]
which means our new equivalent system is:
[tex]$
\begin{array}{l}
-2x + 4y = 8 \\
2x + 4y = 32
\end{array}
$[/tex]
Thus, the correct action is:
Divide the first equation, [tex]\(-4x + 8y = 16\)[/tex], by 2.
