Answer: The correct option is (A) -28.
Step-by-step explanation: The given system of linear equations is as follows :
[tex]3x+y-10=0,\\\\4x-y-4=0.[/tex]
We are to find the y-determinant for the above system of equations.
The given system can be written as :
[tex]3x+y=10~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\4x-y=4~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Therefore, the y-determinant of the system will be
[tex]D=\begin{vmatrix}3 & 4\\ 10 & 4\end{vmatrix}=3\times4-4\times10=12-40=-28.[/tex]
Thus, the required value of the y-determinant is -28.
Option (A) is CORRECT.
