Sure, let's solve the given system of equations and represent them in matrix form. We'll use the equations provided:
1. [tex]\( y = 700x + 200 \)[/tex]
2. [tex]\( y = 5000 - 75x \)[/tex]
First, we'll convert each equation to standard form [tex]\( Ax + By = C \)[/tex].
### Equation 1:
[tex]\( y = 700x + 200 \)[/tex]
Rearrange it to the standard form:
[tex]\[ y - 700x = 200 \][/tex]
This can be written in the form of:
[tex]\[ -700x + y = 200 \][/tex]
So, the corresponding row for the matrix will be:
[tex]\[ [-700, 1, 200] \][/tex]
### Equation 2:
[tex]\( y = 5000 - 75x \)[/tex]
Rearrange it to the standard form:
[tex]\[ y + 75x = 5000 \][/tex]
This can be written in the form of:
[tex]\[ 75x + y = 5000 \][/tex]
So, the corresponding row for the matrix will be:
[tex]\[ [75, 1, 5000] \][/tex]
Now, let's assemble the matrix using rows from the equations above:
[tex]\[
\begin{array}{ccc}
-700 & 1 & 200 \\
75 & 1 & 5000 \\
\end{array}
\][/tex]
Therefore, the completed matrix representing the given system of equations is:
[tex]\[
\left[\begin{array}{ccc}
-700 & 1 & 200 \\
75 & 1 & 5000 \\
\end{array}\right]
\][/tex]
This matrix succinctly holds the coefficients and constants from the system of equations given.
