Answer: The correct option is (a). - 5.
Step-by-step explanation: We are given to find the value of the system determinant for the following system of linear equations :
[tex]x+2y=5,\\\\x-3y=7.[/tex]
The system determinant for the above system is written as
[tex]\begin{vmatrix}1 & 2\\ 1 & -3\end{vmatrix}[/tex]
And, its value will be
[tex]\begin{vmatrix}1 & 2\\ 1 & -3\end{vmatrix}=1\times (-3)-2\times 1=-3-2=-5.[/tex]
Thus, the required value is - 5.
Option (a) is CORRECT.
