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The Following System Does Not Have a Unique Solution {2x+3y+z=243xy+5z=8x+2y+6z=16\left\{ \begin{array} { c } - 2 x + 3 y + z = - 24 \\3 x - y + 5 z = 8 \\x + 2 y + 6 z = - 16 \\\end{array} \right.

Question 3

Multiple Choice

The following system does not have a unique solution. Solve the system.
- {2x+3y+z=243xy+5z=8x+2y+6z=16\left\{ \begin{array} { c } - 2 x + 3 y + z = - 24 \\3 x - y + 5 z = 8 \\x + 2 y + 6 z = - 16 \\\end{array} \right.


A) x = 0 , y = - 8 , z = 0
B) infinitely many solutions of the form x=167z,y=8137z,z=zx = - \frac { 16 } { 7 } z , y = - 8 - \frac { 13 } { 7 } z , z = z
C) inconsistent system, no solution
D) x=167,y=437,z=1x = - \frac { 16 } { 7 } , y = \frac { 43 } { 7 } , z = 1

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