Solve the system of equations.
-$$\left\{ \begin{aligned}
- x + y + 2 z & = 0 \
x + 2 y + z & = 6 \
- 2 x - y + z & = - 6
\end{aligned} \right.$$
A) inconsistent (no solution)
B) $x = 2 - z$
$y = z + 2$
$z =$ any real number
C) $x = z + 2$
$y = 2 - z$
$z =$ any real number

D) $x = z + 2$
$y = z - 2$
$z =$ any real number

Question

Solve the system of equations.
-$$\left\{ \begin{aligned}
- x + y + 2 z & = 0 \
x + 2 y + z & = 6 \
- 2 x - y + z & = - 6
\end{aligned} \right.$$
A) inconsistent (no solution)
B) $x = 2 - z$
$y = z + 2$
$z =$ any real number
C) $x = z + 2$
$y = 2 - z$
$z =$ any real number

D) $x = z + 2$
$y = z - 2$
$z =$ any real number

Quizplus · Accepted Answer

The system of equations is consistent and dependent, leading to a parametric solution where $x = z + 2$, $y = 2 - z$, and $z$ can be any real number.

Solve the System of Equations {−x+y+2z=0x+2y+z=6−2x−y+z=−6\left\{ \begin{aligned}- x + y + 2 z & = 0 \\x + 2 y + z & = 6 \\- 2 x - y + z & = - 6\end{aligned} \right.⎩⎨⎧​−x+y+2zx+2y+z−2x−y+z​=0=6=−6​

Solve the System of Equations $\left\{ \begin{aligned}- x + y + 2 z & = 0 \\x + 2 y + z & = 6 \\- 2 x - y + z & = - 6\end{aligned} \right.$