Question

Choose the value of the y determinant (Dy) in the following system.
5x – y = 3
2x + 4y = 7

Answer 1

First write out the coefficient matrix:\[A=\left[\begin{matrix}5 & -1 \\ 2 & 4\end{matrix}\right]\]name the vector of the right-hand-sides::\[b=\left(\begin{matrix}3 \\ 7\end{matrix}\right)\]The x-determinant is found by replacing the first column of the coefficient matrix A with b and taking the determinant.
The y-determinant is found by replacing the second column of A by b and taking the determinant.

Answer 2

29

22

19

41

Answer 3

in general we have for\[A=\left[\begin{matrix}a_{11} & a_{12} \\ a_{21} & a_{22}\end{matrix}\right]\]\[b=\left(\begin{matrix}b_1 \\ b_2\end{matrix}\right)\]that the x-determinant is\[D_x=\det\left[\begin{matrix}b_{1} & a_{12} \\ b_{2} & a_{22}\end{matrix}\right]\]and the y-determinant is\[D_y=\det\left[\begin{matrix}a_{11} & b_{1} \\ a_{21} & b_{2}\end{matrix}\right]\]