# Math Help - Cramer's Rule

1. ## Cramer's Rule

Solve the following system; if the system is inconsistent say so. Use Cramer's Rule to obtain solution.

-9x + -4y + -6z = 85

-16x + -6y + 37z = 81

-7x + 8y + -4z = 75.

I am able to work this when there is just two sets of equations but I am having trouble figuring out three of them.

2. \begin{aligned} \bold{Ax} & = \bold{B} \\ \left[\begin{array}{ccc} -9 & -4 & -6 \\ -16 & -6 & 37 \\ -7 & 8 & -4 \end{array}\right] \begin{bmatrix} x \\ y \\ z \end{bmatrix} & = {\color{red}\begin{bmatrix} 85 \\ 81 \\ 75 \end{bmatrix} }\end{aligned}

Cramer's Rule says that:

$x = \frac{\left| \begin{array}{ccc} {\color{red}85} & -4 & -6 \\ {\color{red}81} & -6 & 37 \\ {\color{red}75} & 8 & -4 \end{array} \right|}{\det (A)}$..... $y = \frac{\left|\begin{array}{ccc} -9 & {\color{red}85} & -6 \\ -16 & {\color{red}81} & 37 \\ -7 & {\color{red}75} & -4 \end{array}\right|}{\det (A)}$..... $z = \frac{\left| \begin{array}{ccc} -9 & -4 & {\color{red}85} \\ -16 & -6 & {\color{red}81} \\ -7 & 8 & {\color{red}75} \end{array}\right|}{\det (A)}$