Solve the system of linear equations.
$$\left\{ \begin{aligned}
2 x - 2 y + 3 z & = - 21 \
2 x + z & = - 11 \
- 2 x + 4 y - 4 z & = 28
\end{aligned} \right.$$
A) $( 3 , - 3,4 )$
B) $( - 4,2 , - 3 )$
C) $( 2 , - 3 , - 4 )$
D) $( - 3,4,3 )$
E) $( - 4,2,6 )$

Question

Quizplus · Accepted Answer

To solve the system of equations, we can use either substitution or elimination method. Adding the first and third equations cancels out $x$ and $y$, simplifying the system. Substituting the value of $z$ from the second equation into the other equations helps find $x$ and $y$. The correct solution is $(-4, 2, -3)$.

Solve the System of Linear Equations {2x−2y+3z=−212x+z=−11−2x+4y−4z=28\left\{ \begin{aligned}2 x - 2 y + 3 z & = - 21 \\2 x + z & = - 11 \\- 2 x + 4 y - 4 z & = 28\end{aligned} \right.⎩⎨⎧​2x−2y+3z2x+z−2x+4y−4z​=−21=−11=28​

Solve the System of Linear Equations $\left\{ \begin{aligned}2 x - 2 y + 3 z & = - 21 \\2 x + z & = - 11 \\- 2 x + 4 y - 4 z & = 28\end{aligned} \right.$