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Dakarai wrote the system of linear equations below:

[tex]\[
\begin{aligned}
7x + 8y &= 28 \\
-3x + 9y &= -24
\end{aligned}
\][/tex]

Dakarai then wrote the coefficient matrix that represents this system. Which matrix could she have written?

A. [tex]\(\left[\begin{array}{cc} 7 & 8 \\ -3 & 9 \end{array}\right]\)[/tex]

B. [tex]\(\left[\begin{array}{cc} 7 & -3 \\ 8 & 9 \end{array}\right]\)[/tex]

C. [tex]\(\left[\begin{array}{ccc} 7 & 8 & 28 \\ -3 & 9 & -24 \end{array}\right]\)[/tex]

Sagot :

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]