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

1. TuringTest

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.

2. anonymous

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3. TuringTest

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]$

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