Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$x+4 y-z=3$
$-4 x-16 y+4 z=-12$
$3 \mathrm{x}+12 \mathrm{y}-3 \mathrm{z}=9$

A) $\{(0,2,5)\}$
B) $\{(1,1,2)\}$
C) $\varnothing ;$ inconsistent system
D) $\{(x, y, z) \mid x+4 y-z=3\}$; dependent equations

Question

Solve the system of equations. If the system is inconsistent or has dependent equations, say so.
-$x+4 y-z=3$
$-4 x-16 y+4 z=-12$
$3 \mathrm{x}+12 \mathrm{y}-3 \mathrm{z}=9$

A) $\{(0,2,5)\}$
B) $\{(1,1,2)\}$
C) $\varnothing ;$ inconsistent system
D) $\{(x, y, z) \mid x+4 y-z=3\}$; dependent equations

Quizplus · Accepted Answer

The second and third equations are multiples of the first equation, indicating that all three equations actually represent the same plane in three-dimensional space. This means there is an infinite number of solutions that satisfy the given condition $x+4y-z=3$, indicating the system has dependent equations.

Solve the System of Equations x+4y−z=3x+4 y-z=3x+4y−z=3 −4x−16y+4z=−12-4 x-16 y+4 z=-12−4x−16y+4z=−12

Solve the System of Equations $x+4 y-z=3$ $-4 x-16 y+4 z=-12$