Let's examine the given problem and determine the correct system of equations.
### Problem Statement
1. The hardcover version of a book weighs twice as much as its paperback version.
2. The hardcover book and the paperback together weigh 4.2 pounds.
Let's denote:
- [tex]\( h \)[/tex] as the weight of the hardcover book.
- [tex]\( p \)[/tex] as the weight of the paperback book.
From the problem statement, we can infer the following equations:
1. The hardcover book weighs twice as much as the paperback version. This can be written as:
[tex]\[
h = 2p
\][/tex]
2. The total weight of the hardcover book and the paperback book is 4.2 pounds. This can be written as:
[tex]\[
h + p = 4.2
\][/tex]
Now, we need to examine the given options and see which system of equations matches our inferences.
### Options Analysis
1. [tex]\(\begin{array}{l}
h=p-4.2 \\
h=2p
\end{array}\)[/tex]
The first equation [tex]\(h = p - 4.2\)[/tex] does not align with our inference that [tex]\( h + p = 4.2 \)[/tex]. Therefore, this is not the correct system.
2. [tex]\(\begin{array}{l}
h=4.2-p \\
p=2h
\end{array}\)[/tex]
The second equation [tex]\(p = 2h\)[/tex] does not align with our inference that [tex]\(h = 2p\)[/tex]. Therefore, this is not the correct system.
3. [tex]\(\begin{array}{l}
h=p-4.2 \\
p=2h
\end{array}\)[/tex]
Neither of these equations aligns with our inferences. Therefore, this is not the correct system.
4. [tex]\(\begin{array}{l}
h=4.2-p \\
h=2p
\end{array}\)[/tex]
Both equations align perfectly with our inferences:
- [tex]\(h = 4.2 - p\)[/tex] represents the total weight equation rearranged.
- [tex]\(h = 2p\)[/tex] represents the relationship between the weights of the hardcover and paperback versions.
Therefore, the correct system of equations to use is:
[tex]\[
\begin{array}{l}
h=4.2-p \\
h=2 p
\end{array}
\][/tex]
This correctly models our problem statement and will allow us to solve for [tex]\(h\)[/tex] and [tex]\(p\)[/tex].
