In order to determine which coefficient matrix correctly represents the given system of linear equations, we need to clarify what a coefficient matrix is. A coefficient matrix is a matrix that contains only the coefficients of the variables from the system of equations, and does not include the constants from the right-hand side of the equations.
Let's look at the system of equations provided:
[tex]\[
\begin{aligned}
7x + 8y &= 28 \\
-3x + 9y &= -24
\end{aligned}
\][/tex]
Here, the coefficients of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are extracted from each equation:
1. From the first equation [tex]\( 7x + 8y = 28 \)[/tex], the coefficients are [tex]\( 7 \)[/tex] and [tex]\( 8 \)[/tex].
2. From the second equation [tex]\( -3x + 9y = -24 \)[/tex], the coefficients are [tex]\( -3 \)[/tex] and [tex]\( 9 \)[/tex].
By arranging these coefficients into a matrix, each row will correspond to the coefficients of one equation, and each element in a row will correspond to the coefficients of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] respectively:
[tex]\[
\left[\begin{array}{cc}
7 & 8 \\
-3 & 9
\end{array}\right]
\][/tex]
Therefore, the correct coefficient matrix that Dakarai could have written is:
[tex]\[
\left[\begin{array}{cc}
7 & 8 \\
-3 & 9
\end{array}\right]
\][/tex]
