Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l }
- 4 x - 6 y - 8 z = - 84 \
- 4 x + 4 y - 3 z = 11 \
- 9 x - 5 y - 9 z = - 94
\end{array} \right.$$
A) $x = 3 , y = 8 , z = 3$
B) $x = 4 , y = 6 , z = 3$
C) $x = 8 , y = 3 , z = 8$
D) $x = 3 , y = - 8 , z = - 3$

Question

Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l } 
- 4 x - 6 y - 8 z = - 84 \
- 4 x + 4 y - 3 z = 11 \
- 9 x - 5 y - 9 z = - 94
\end{array} \right.$$
A) $x = 3 , y = 8 , z = 3$
B) $x = 4 , y = 6 , z = 3$
C) $x = 8 , y = 3 , z = 8$
D) $x = 3 , y = - 8 , z = - 3$

Quizplus · Accepted Answer

Cramer's rule involves calculating determinants of matrices. For this system, the determinant of the coefficient matrix and the determinants of matrices formed by replacing one column of the coefficient matrix with the constants on the right-hand side of the equations are used to find the values of x, y, and z. The correct solution using Cramer's rule is $x = 3$, $y = 8$, $z = 3$.