Answer
Coefficient Matrix $=\begin{bmatrix} 3 & -1 \\ 1 & 0\end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} x \\
y\end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 7 \\ 2\end{bmatrix}$
Our matrix equation is:
$\begin{bmatrix} 3 & -1 \\ 1 & 0 \end{bmatrix} \begin{bmatrix} x \\
y\end{bmatrix} =\begin{bmatrix} 7 \\ 2 \end{bmatrix}$
Work Step by Step
Write the given system of equations into the matrix form in order to label the parts of the matrix equation.
Re-arrange the given system of equations as follows: $$3x-y=7 \\ x+(0)y=2$$
Our matrix equation is:
$\begin{bmatrix} 3 & -1 \\ 1 & 0 \end{bmatrix} \begin{bmatrix} x \\
y\end{bmatrix} =\begin{bmatrix} 7 \\ 2 \end{bmatrix}$
Our required results are:
Coefficient Matrix $=\begin{bmatrix} 3 & -1 \\ 1 & 0\end{bmatrix} $;
Variable Matrix $=\begin{bmatrix} x \\
y\end{bmatrix}$;
and
Constant Matrix $=\begin{bmatrix} 7 \\ 2\end{bmatrix}$
