If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l }
5 x - y + z = 8 \
7 x + y + z = 6
\end{array}$$
$$12 x + 2 z = 14$$
A) $\{ ( x , - x - 1 , - 6 x + 7 ) \}$
B) $\{ ( x , - x + 1,6 x - 7 ) \}$
C) $\{ ( x , - x + 1 , - 6 x + 7 ) \}$
D) $\{ ( x , - x + 1,6 x + 7 ) \}$

Question

If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l } 
5 x - y + z = 8 \
7 x + y + z = 6
\end{array}$$
$$12 x + 2 z = 14$$
A) $\{ ( x , - x - 1 , - 6 x + 7 ) \}$
B) $\{ ( x , - x + 1,6 x - 7 ) \}$
C) $\{ ( x , - x + 1 , - 6 x + 7 ) \}$
D) $\{ ( x , - x + 1,6 x + 7 ) \}$

Quizplus · Accepted Answer

The system has infinitely many solutions because the third equation is a linear combination of the first two equations. The solution set can be written as $\{ ( x , - x - 1 , - 6 x + 7 ) \}$, where x is arbitrary.

If the System Has Infinitely Many Solutions, Write the Solution 5x−y+z=87x+y+z=6\begin{array} { l } 5 x - y + z = 8 \\7 x + y + z = 6\end{array}5x−y+z=87x+y+z=6​

If the System Has Infinitely Many Solutions, Write the Solution $\begin{array} { l } 5 x - y + z = 8 \\7 x + y + z = 6\end{array}$