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Type the correct answer in each box. Use numerals instead of words.

This system of equations has been placed in a matrix:

[tex]\[ \begin{array}{l}
y = 650x + 175 \\
y = 25,080 - 120x
\end{array} \][/tex]

[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
& & \text{Column 1} & & \text{Column 2} & & \text{Column 3} & \\
\hline
\hline & & & & & & \\
\hline
\hline \text{Row 1} & & \square & & -1 & & \square \\
\hline
\hline & & & & & & \\
\hline
\hline \text{Row 2} & & 120 & & \square & & \\
\hline
\hline & & & & & & \\
\hline
\end{array}
\][/tex]


Sagot :

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]