If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { r }
4 x + y + z = 2 \
x - y + 5 z = 8 \
4 x + y + z = 11
\end{array}$$
A) $\{ ( 2,3 , - 3 ) \}$
B) $\varnothing$
C) $\{ ( 2 , - 3,3 ) \}$
D) $\{ ( 3 , - 3,2 ) \}$

Question

If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { r } 
4 x + y + z = 2 \
x - y + 5 z = 8 \
4 x + y + z = 11
\end{array}$$
A) $\{ ( 2,3 , - 3 ) \}$
B) $\varnothing$
C) $\{ ( 2 , - 3,3 ) \}$
D) $\{ ( 3 , - 3,2 ) \}$

Quizplus · Accepted Answer

The system cannot have infinitely many solutions because the first and third equations are contradictory (they have the same left-hand side but different right-hand sides), indicating that the system has no solution.

If the System Has Infinitely Many Solutions, Write the Solution 4x+y+z=2x−y+5z=84x+y+z=11\begin{array} { r } 4 x + y + z = 2 \\x - y + 5 z = 8 \\4 x + y + z = 11\end{array}4x+y+z=2x−y+5z=84x+y+z=11​

If the System Has Infinitely Many Solutions, Write the Solution $\begin{array} { r } 4 x + y + z = 2 \\x - y + 5 z = 8 \\4 x + y + z = 11\end{array}$