Solve the system using determinants.
-$$\begin{array} { l }
3 x + 4 y - z = 42 \
x - 4 y + 5 z = - 2 \
2 x + y + z = 23
\end{array}$$
A)(4, 9, 6)
B)(4, -9, -6)
C)(5, 7, 6)
D)(9, 6, 9)

Question

Solve the system using determinants.
-$$\begin{array} { l } 
3 x + 4 y - z = 42 \
x - 4 y + 5 z = - 2 \
2 x + y + z = 23
\end{array}$$
A)(4, 9, 6)
B)(4, -9, -6)
C)(5, 7, 6)
D)(9, 6, 9)

Quizplus · Accepted Answer

To solve the system using determinants, we use Cramer's Rule. First, find the determinant of the coefficient matrix (D), then find the determinants of matrices formed by replacing one column of the coefficient matrix with the constants on the right side of the equations (Dx, Dy, Dz) for x, y, and z respectively. The solutions are x = Dx/D, y = Dy/D, and z = Dz/D. Calculating these determinants and solving gives the solution (4, 9, 6).

Solve the System Using Determinants 3x+4y−z=42x−4y+5z=−22x+y+z=23\begin{array} { l } 3 x + 4 y - z = 42 \\x - 4 y + 5 z = - 2 \\2 x + y + z = 23\end{array}3x+4y−z=42x−4y+5z=−22x+y+z=23​

Solve the System Using Determinants $\begin{array} { l } 3 x + 4 y - z = 42 \\x - 4 y + 5 z = - 2 \\2 x + y + z = 23\end{array}$