Solve the system of equations.
-$$\left\{ \begin{aligned}
2 x - y + 5 z & = - 7 \
x + y - 2 z & = - 2 \
x - y + 4 z & = 8
\end{aligned} \right.$$

A) $x = - 3 - z$
$y = z - 3$
$y = 3 z + 1$
$z =$ any real number

B) $x = 3 z + 1$
$y = z - 3$
$z =$ any real number

C) $x = z + 3$
$y = 3 z + 1$
$z =$ any real number

D) inconsistent (no solution)

Question

Solve the system of equations.
-$$\left\{ \begin{aligned}
2 x - y + 5 z & = - 7 \
x + y - 2 z & = - 2 \
x - y + 4 z & = 8
\end{aligned} \right.$$

A) $x = - 3 - z$
$y = z - 3$
$y = 3 z + 1$
$z =$ any real number

B) $x = 3 z + 1$
$y = z - 3$
$z =$ any real number

C) $x = z + 3$
$y = 3 z + 1$
$z =$ any real number

D) inconsistent (no solution)

Quizplus · Accepted Answer

The system of equations can be solved by row reduction. The augmented matrix is:$$\left[ \begin{array}{rrr|r}2 & -1 & 5 & -7 \1 & 1 & -2 & -2 \1 & -1 & 4 & 8\end{array} ight]$$Row reducing the matrix gives:$$\left[ \begin{array}{rrr|r}1 & 0 & 3 & -3 \0 & 1 & -3 & -1 \0 & 0 & 1 & 3\end{array} ight]$$So the solution is:$$x = -3 - 3z$$$$y = -z - 1$$$$z = 	ext{any real number}$$

Solve the System of Equations {2x−y+5z=−7x+y−2z=−2x−y+4z=8\left\{ \begin{aligned}2 x - y + 5 z & = - 7 \\x + y - 2 z & = - 2 \\x - y + 4 z & = 8\end{aligned} \right.⎩⎨⎧​2x−y+5zx+y−2zx−y+4z​=−7=−2=8​

Solve the System of Equations $\left\{ \begin{aligned}2 x - y + 5 z & = - 7 \\x + y - 2 z & = - 2 \\x - y + 4 z & = 8\end{aligned} \right.$