The system of equations 3x + 4y = 5, 6x + 7y = -8 is written in matri…

The correct answer is Option 3: $\begin{bmatrix} 3 & 4 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ -8 \end{bmatrix}$

Let the system be:

$\begin{cases} 3x + 4y = 5 \\ 6x + 7y = -8 \end{cases}$

Matrix form

A system of linear equations can be written as:

$AX = B$

where

$A = \begin{bmatrix} 3 & 4 \\ 6 & 7 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \end{bmatrix}, \quad B = \begin{bmatrix} 5 \\ -8 \end{bmatrix}$

Hence, the matrix form is:

$\begin{bmatrix} 3 & 4 \\ 6 & 7 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ -8 \end{bmatrix}$