Solve a System of Linear Equations in Three Variables Using Cramer's Rule
-$$\begin{array} { l }
3 x + 7 z = 31 \
5 x + 3 y + 2 z = 34 \
- 9 x - 5 y \quad = - 44
\end{array}$$
A) $\{ ( 1,7,4 ) \}$
B) $\{ ( 7,4,7 ) \}$
C) $\{ ( 1 , - 7 , - 4 ) \}$
D) $\{ ( 2,5,4 ) \}$

Question

Solve a System of Linear Equations in Three Variables Using Cramer's Rule
-$$\begin{array} { l } 
3 x + 7 z = 31 \
5 x + 3 y + 2 z = 34 \
- 9 x - 5 y \quad = - 44
\end{array}$$
A) $\{ ( 1,7,4 ) \}$
B) $\{ ( 7,4,7 ) \}$
C) $\{ ( 1 , - 7 , - 4 ) \}$
D) $\{ ( 2,5,4 ) \}$

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 with substituted columns give the solution (1,7,4), matching choice A.

Solve a System of Linear Equations in Three Variables Using 3x+7z=315x+3y+2z=34−9x−5y=−44\begin{array} { l } 3 x + 7 z = 31 \\5 x + 3 y + 2 z = 34 \\- 9 x - 5 y \quad = - 44\end{array}3x+7z=315x+3y+2z=34−9x−5y=−44​

Solve a System of Linear Equations in Three Variables Using $\begin{array} { l } 3 x + 7 z = 31 \\5 x + 3 y + 2 z = 34 \\- 9 x - 5 y \quad = - 44\end{array}$