Solve the system using determinants.
-$$\begin{array} { l }
- 2 x + 4 y - z = 19 \
x - 9 y - 5 z = - 82 \
5 x + y + z = 36
\end{array}$$
A)(5, 8, 3)
B)(8, 3, 8)
C)(6, 6, 3)
D)(5, -8, -3)

Question

Solve the system using determinants.
-$$\begin{array} { l } 
- 2 x + 4 y - z = 19 \
x - 9 y - 5 z = - 82 \
5 x + y + z = 36
\end{array}$$
A)(5, 8, 3)
B)(8, 3, 8)
C)(6, 6, 3)
D)(5, -8, -3)

Quizplus · Accepted Answer

To solve the system using determinants, we use Cramer's Rule. First, we find the determinant of the coefficient matrix (D), and then the determinants of matrices obtained by replacing one column of the coefficient matrix at a time with the column of constants (Dx, Dy, Dz). The solutions are x = Dx/D, y = Dy/D, and z = Dz/D. Calculating these determinants and solving gives the solution (5, 8, 3).

Solve the System Using Determinants −2x+4y−z=19x−9y−5z=−825x+y+z=36\begin{array} { l } - 2 x + 4 y - z = 19 \\x - 9 y - 5 z = - 82 \\5 x + y + z = 36\end{array}−2x+4y−z=19x−9y−5z=−825x+y+z=36​

Solve the System Using Determinants $\begin{array} { l } - 2 x + 4 y - z = 19 \\x - 9 y - 5 z = - 82 \\5 x + y + z = 36\end{array}$