Solve the system.
$\begin{array} { l }
4 x + 5 y + z = - 33 \
5 x - 3 y - z = - 9 \
3 x + y + 4 z = - 23
\end{array}$
A) $\{ ( - 4 , - 3 , - 2 ) \}$
B) $\{ ( - 2 , - 3 , - 4 ) \}$
C) $\{ ( - 4 , - 2 , - 3 ) \}$
D) $\varnothing$

Question

Solve the system.
$\begin{array} { l } 
4 x + 5 y + z = - 33 \
5 x - 3 y - z = - 9 \
3 x + y + 4 z = - 23
\end{array}$
A) $\{ ( - 4 , - 3 , - 2 ) \}$
B) $\{ ( - 2 , - 3 , - 4 ) \}$
C) $\{ ( - 4 , - 2 , - 3 ) \}$
D) $\varnothing$

Quizplus · Accepted Answer

To solve the system of equations, you can use methods such as substitution, elimination, or matrix operations. Adding the first two equations cancels out $z$, and you can then solve the resulting system for $x$ and $y$. Substituting these values back into one of the original equations allows you to solve for $z$. After solving, you find that the solution is $x = -4$, $y = -3$, and $z = -2$, which corresponds to choice A.

Solve the System 4x+5y+z=−335x−3y−z=−93x+y+4z=−23\begin{array} { l } 4 x + 5 y + z = - 33 \\5 x - 3 y - z = - 9 \\3 x + y + 4 z = - 23\end{array}4x+5y+z=−335x−3y−z=−93x+y+4z=−23​

Solve the System $\begin{array} { l } 4 x + 5 y + z = - 33 \\5 x - 3 y - z = - 9 \\3 x + y + 4 z = - 23\end{array}$