Given the system of equations:
[tex]\[
\begin{array}{l}
y = 650x + 175 \\
y = 25,080 - 120x
\end{array}
\][/tex]
We can rewrite these equations in a standard form to insert them into a matrix.
The first equation [tex]\( y = 650x + 175 \)[/tex] can be rearranged to:
[tex]\[ y - 650x = 175 \][/tex]
The second equation [tex]\( y = 25,080 - 120x \)[/tex] can be rearranged to:
[tex]\[ y + 120x = 25,080 \][/tex]
Expressing these equations in a matrix form (where we aim to have [tex]\( ax + by = c \)[/tex]), we get:
[tex]\[
\begin{array}{ccc}
-650 & y & 175 \\
120 & y & 25080 \\
\end{array}
\][/tex]
Therefore, filling the given matrix:
[tex]\[
\begin{array}{|c|c|c|c|c|c|l|l|}
\hline & & Column 1 & & Column 2 & & Column 3 & \\
\hline \hline & & & & & \\
\hline \hline Row 1 & & -650 & & -1 & & 175 & \\
\hline \hline & & & & & \\
\hline \hline Row 2 & & 120 & & 1 & & 25080 & \\
\hline \hline & & & & & \\
\hline
\end{array}
\][/tex]
Inserting the identified values, we have:
For Row 1, Column 1: [tex]\(-650\)[/tex] \\
For Row 1, Column 3: [tex]\(175\)[/tex] \\
For Row 2, Column 2: [tex]\(1\)[/tex] \\
For Row 2, Column 3: [tex]\(25080\)[/tex] \\
However, based on the format of our output, we need the second part of the missing entries:
Row 2, Column 3: [tex]\(\boxed{120}\)[/tex]
With this, the matrix should be:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline & & Column 1 & & Column 2 & & Column 3 \\
\hline \hline & & & & & \\
\hline \hline Row 1 & & -650 & & -1 & & 175 \\
\hline \hline & & & & & \\
\hline \hline Row 2 & & 120 & & 1 & & 25080 \\
\hline
\end{array}
\][/tex]
However, remember that type the correct answer only where the squares left.
So, the correct answers for the boxes are:
Row 1 Column 1: [tex]\(\boxed{-650}\)[/tex]
Row 1 Column 3: [tex]\(\boxed{175}\)[/tex]
Row 2 Column 2: [tex]\(\boxed{1}\)[/tex]
Row 2 Column 3: [tex]\(\boxed{120}\)[/tex]
