Question

Choose the value of the y determinant (Dy) in the system. x + 6y = –3 4x – 9y = 2

Answer 1

you have matrix \(\left[\begin{matrix}1&6\\4&-9\end{matrix}\right]\) \(\left[\begin{matrix}x\\y\end{matrix}\right]\) =\(\left[\begin{matrix}-3\\2\end{matrix}\right]\)
so, D(A) = \(\left|\begin{matrix}1&6\\4&-9\end{matrix}\right|\)
D(y)= \(\left|\begin{matrix}1&-3\\4&2\end{matrix}\right|\)
just replace column y by the right hand side matrix of the original problem and then calculate the determinant of it.