Answer: The value of the determinant is 1.
Step-by-step explanation: The given system of linear equation is as follows:
[tex]6x+y=4~~~~~~~~~~~~~~~~(i)\\\\5x-y-7=0\\\\\Rightarrow 5x-y=7~~~~~~~~~~~(ii)[/tex]
The first column of the determinant gives the coefficients of 'x' and the second column gives the coefficients of y in the two equations.
Therefore, the determinant for the given system is
[tex]D=\begin{vmatrix} 6& 1\\ 5& 1\end{vmatrix}=6\times 1-5\times 1=6-5=1.[/tex]
Thus, the required value of the determinant is 1.
