Write the system as a matrix equation of the form AX = B.
-8 4

Question

Quizplus · Accepted Answer

The given system is:
8x + 4y = 11
-2x + 5y = 7

We can write this in the form of AX = B, where A is the coefficient matrix of x and y, X is the column matrix of x and y, and B is the constant matrix of the system.
A = \begin{pmatrix} 8 & 4 \ -2 & 5 \end{pmatrix}, X = \begin{pmatrix} x \ y \end{pmatrix}, B = \begin{pmatrix} 11 \ 7 \end{pmatrix}

So, the matrix equation AX = B is:
\begin{pmatrix} 8 & 4 \ -2 & 5 \end{pmatrix}\begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 11 \ 7 \end{pmatrix} The system can be written as:
$$\begin{pmatrix}8 & 4\ -3 & 5\end{pmatrix} \begin{pmatrix}x \y\end{pmatrix} = \begin{pmatrix}-2 \ 3\end{pmatrix}$$
Therefore, in matrix form, the system is represented as $AX=B$, where:
$$A=\begin{pmatrix}8 & 4\ -3 & 5\end{pmatrix}, X=\begin{pmatrix}x\y\end{pmatrix}, B=\begin{pmatrix}-2\3\end{pmatrix}$$
The correct choice is A, as it matches the format of the matrix entries.

Write the System as a Matrix Equation of the Form