Let's analyze the given system of equations and the corresponding matrix representation of the system.
We have the system of equations:
[tex]\[
\begin{array}{l}
3x - 4y = -9 \\
7y = 24
\end{array}
\][/tex]
To write this as a matrix equation, we need to represent it in the form [tex]\( A \mathbf{x} = \mathbf{b} \)[/tex], where [tex]\(A\)[/tex] is the coefficient matrix, [tex]\(\mathbf{x}\)[/tex] is the column matrix of variables, and [tex]\(\mathbf{b}\)[/tex] is the constant matrix.
Given the system:
[tex]\[
\begin{array}{l}
3x - 4y = -9 \\
7y = 24
\end{array}
\][/tex]
We identify the coefficients of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] for each equation and place them in a matrix [tex]\( A \)[/tex]. The variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] form the column matrix [tex]\(\mathbf{x}\)[/tex], and the constants on the right side of the equations form the matrix [tex]\(\mathbf{b}\)[/tex].
From the system above, we have:
[tex]\[
A = \begin{pmatrix}
3 & -4 \\
0 & 7
\end{pmatrix}
\][/tex]
The column matrix of variables is:
[tex]\[
\mathbf{x} = \begin{pmatrix}
x \\
y
\end{pmatrix}
\][/tex]
And the constant matrix is:
[tex]\[
\mathbf{b} = \begin{pmatrix}
-9 \\
24
\end{pmatrix}
\][/tex]
So the matrix equation is:
[tex]\[
\begin{pmatrix}
3 & -4 \\
0 & 7
\end{pmatrix}
\begin{pmatrix}
x \\
y
\end{pmatrix}
=
\begin{pmatrix}
-9 \\
24
\end{pmatrix}
\][/tex]
Comparing this with the given options, we find that the correct answer is:
[tex]\[
\left[\begin{array}{cc}3 & -4 \\ 0 & 7\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}-9 \\ 24\end{array}\right]
\][/tex]
