If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{aligned}
4 x + y + z & = 6 \
x - y + 2 z & = 12 \
4 x + y + z & = 21
\end{aligned}$$
A) $\{ ( 4,5 , - 3 ) \}$
B) $\{ ( 4 , - 3,5 ) \}$
C) $\varnothing$
D) $\{ ( 5 , - 3,4 ) \}$

Question

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). This inconsistency means there are no solutions.

If the System Has Infinitely Many Solutions, Write the Solution 4x+y+z=6x−y+2z=124x+y+z=21\begin{aligned}4 x + y + z & = 6 \\x - y + 2 z & = 12 \\4 x + y + z & = 21\end{aligned}4x+y+zx−y+2z4x+y+z​=6=12=21​

If the System Has Infinitely Many Solutions, Write the Solution $\begin{aligned}4 x + y + z & = 6 \\x - y + 2 z & = 12 \\4 x + y + z & = 21\end{aligned}$