The following system does not have a unique solution. Solve the system.
-$$\left\{ \begin{array} { c }
x - y + z = 8 \
x + y + z = 6 \
3 x + y + 3 z = 10
\end{array} \right.$$
A) $x = - 2 , y = 1 , z = 9$
B) $x = 7 , y = - 1 , z = 0$
C) inconsistent system, no solution
D) $x = 5 , y = 3 , z = 6$

Question

The following system does not have a unique solution. Solve the system.
-$$\left\{ \begin{array} { c } 
x - y + z = 8 \
x + y + z = 6 \
3 x + y + 3 z = 10
\end{array} \right.$$
A) $x = - 2 , y = 1 , z = 9$
B) $x = 7 , y = - 1 , z = 0$
C) inconsistent system, no solution
D) $x = 5 , y = 3 , z = 6$

Quizplus · Accepted Answer

The system is inconsistent because adding the first two equations gives $2x + 2z = 14$, or $x + z = 7$. Subtracting the first equation from the second gives $2y = -2$, or $y = -1$. Substituting $y = -1$ into the second equation gives $x + z = 7$, which is consistent with our earlier finding. However, substituting $y = -1$ into the third equation gives $3x + 3z = 13$, which contradicts the earlier result of $x + z = 7$. This inconsistency indicates that the system does not have a solution.

The Following System Does Not Have a Unique Solution {x−y+z=8x+y+z=63x+y+3z=10\left\{ \begin{array} { c } x - y + z = 8 \\x + y + z = 6 \\3 x + y + 3 z = 10\end{array} \right.⎩⎨⎧​x−y+z=8x+y+z=63x+y+3z=10​

The Following System Does Not Have a Unique Solution $\left\{ \begin{array} { c } x - y + z = 8 \\x + y + z = 6 \\3 x + y + 3 z = 10\end{array} \right.$