Solve the system in terms of the arbitrary variable x.
-$$\begin{array} { l }
x - 6 y + z = 10 \
6 x - y - z = 18
\end{array}$$
A) $\{ ( x , x - 4,6 x - 14 ) \}$
B) $\{ ( x , x - 4,5 x ) \}$
C) $\{ ( x , x - 4,5 x - 14 ) \}$
D) $\{ ( 0 , - 4 , - 14 ) \}$

Question

Solve the system in terms of the arbitrary variable x.
-$$\begin{array} { l } 
x - 6 y + z = 10 \
6 x - y - z = 18
\end{array}$$
A) $\{ ( x , x - 4,6 x - 14 ) \}$
B) $\{ ( x , x - 4,5 x ) \}$
C) $\{ ( x , x - 4,5 x - 14 ) \}$
D) $\{ ( 0 , - 4 , - 14 ) \}$

Quizplus · Accepted Answer

To solve the system in terms of the arbitrary variable $x$, we can express $y$ and $z$ in terms of $x$. Adding the two equations, we get $7x - 7y = 28$, which simplifies to $x - y = 4$, or $y = x - 4$. To find $z$, substitute $y = x - 4$ into one of the original equations. Using the first equation, $x - 6(x - 4) + z = 10$, simplifies to $z = 5x - 14$. Therefore, the solution is $\{ ( x , x - 4,5 x - 14 ) \}$.

Solve the System in Terms of the Arbitrary Variable X x−6y+z=106x−y−z=18\begin{array} { l } x - 6 y + z = 10 \\6 x - y - z = 18\end{array}x−6y+z=106x−y−z=18​

Solve the System in Terms of the Arbitrary Variable X $\begin{array} { l } x - 6 y + z = 10 \\6 x - y - z = 18\end{array}$