Solve a System of Linear Equations in Three Variables Using Cramer's Rule
-$$\begin{array} { c }
- 2 x - 2 y - z = - 13 \
x + 6 y + 6 z = 43 \
6 x + y + z = 13
\end{array}$$
A) $\{ ( 1,4,3 ) \}$
B) $\{ ( 4,3,4 ) \}$
C) $\{ ( 1 , - 4 , - 3 ) \}$
D) $\{ ( 2,2,3 ) \}$

Question

Solve a System of Linear Equations in Three Variables Using Cramer's Rule
-$$\begin{array} { c } 
- 2 x - 2 y - z = - 13 \
x + 6 y + 6 z = 43 \
6 x + y + z = 13
\end{array}$$
A) $\{ ( 1,4,3 ) \}$
B) $\{ ( 4,3,4 ) \}$
C) $\{ ( 1 , - 4 , - 3 ) \}$
D) $\{ ( 2,2,3 ) \}$

Quizplus · Accepted Answer

Cramer's Rule involves calculating determinants. The determinant of the coefficient matrix and the determinants with the constants substituted into each column in turn give the solution. For this system, the solution is $\{ ( 1,4,3 ) \}$.

Solve a System of Linear Equations in Three Variables Using −2x−2y−z=−13x+6y+6z=436x+y+z=13\begin{array} { c } - 2 x - 2 y - z = - 13 \\x + 6 y + 6 z = 43 \\6 x + y + z = 13\end{array}−2x−2y−z=−13x+6y+6z=436x+y+z=13​

Solve a System of Linear Equations in Three Variables Using $\begin{array} { c } - 2 x - 2 y - z = - 13 \\x + 6 y + 6 z = 43 \\6 x + y + z = 13\end{array}$