Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$x-y+8 z=-107$
$x+2 y=21$
$2 \mathrm{x}+\mathrm{y}+8 \mathrm{z}=-80$

A) $\varnothing$; inconsistent system
B) $\{(5,8,0)\}$
C) $\{(x, y, z) \mid 2 x+y+8 z=-80\}$; dependent equations
D) $\{(5,8,-13)\}$

Question

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$x-y+8 z=-107$
$x+2 y=21$
$2 \mathrm{x}+\mathrm{y}+8 \mathrm{z}=-80$

A) $\varnothing$; inconsistent system
B) $\{(5,8,0)\}$
C) $\{(x, y, z) \mid 2 x+y+8 z=-80\}$; dependent equations
D) $\{(5,8,-13)\}$

Quizplus · Accepted Answer

The system is inconsistent because subtracting the first equation from the third gives $y=27$, but substituting $y=27$ into the second equation gives $x=-33$, which does not satisfy the first equation when $y=27$ and $x=-33$ are substituted.

Solve the System of Equations x−y+8z=−107x-y+8 z=-107x−y+8z=−107 x+2y=21x+2 y=21x+2y=21 2x+y+8z=−802 \mathrm{x}+\mathrm{y}+8 \mathrm{z}=-802x+y+8z=−80

Solve the System of Equations $x-y+8 z=-107$ $x+2 y=21$ $2 \mathrm{x}+\mathrm{y}+8 \mathrm{z}=-80$