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### Given the following system of equations:

[tex]\[
\begin{array}{l}
-4x + 8y = 16 \\
2x + 4y = 32
\end{array}
\][/tex]

### What action was completed to create this new equivalent system of equations?

[tex]\[
\begin{array}{l}
-2x + 4y = 8 \\
2x + 4y = 32
\end{array}
\][/tex]

A. Divide the second equation, [tex]\(2x + 4y = 32\)[/tex], by 2.

B. Divide the first equation, [tex]\(-4x + 8y = 16\)[/tex], by 2.

C. Multiply the second equation, [tex]\(2x + 4y = 32\)[/tex], by -1.

Sagot :

GinnyAnswer
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.
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