Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l }
9 x - 2 y - z = 64 \
x - 3 y - 3 z = - 27 \
- 6 x + y + z = - 42
\end{array} \right.$$
A) x = 10, y = 3, z = 7
B) x = 9, y = -5, z = -7
C) x = 5, y = 7, z = 5
D) x = 9, y = 5, z = 7

Question

Use Cramer's rule to solve the linear system.
-$$\left\{ \begin{array} { l } 
9 x - 2 y - z = 64 \
x - 3 y - 3 z = - 27 \
- 6 x + y + z = - 42
\end{array} \right.$$
A) x = 10, y = 3, z = 7
B) x = 9, y = -5, z = -7
C) x = 5, y = 7, z = 5
D) x = 9, y = 5, z = 7

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 from the right-hand side are computed. The solution for $x$, $y$, and $z$ using these determinants matches option D: $x = 9$, $y = 5$, $z = 7$.

Use Cramer's Rule to Solve the Linear System {9x−2y−z=64x−3y−3z=−27−6x+y+z=−42\left\{ \begin{array} { l } 9 x - 2 y - z = 64 \\x - 3 y - 3 z = - 27 \\- 6 x + y + z = - 42\end{array} \right.⎩⎨⎧​9x−2y−z=64x−3y−3z=−27−6x+y+z=−42​

Use Cramer's Rule to Solve the Linear System $\left\{ \begin{array} { l } 9 x - 2 y - z = 64 \\x - 3 y - 3 z = - 27 \\- 6 x + y + z = - 42\end{array} \right.$