Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l }
x - 2 y = 8 \
- 3 x + 6 y = - 24
\end{array}$$
A) $\varnothing$
B) $\left. \left\{ x , \frac { x } { 6 } - 4 \right\} \right\}$
C) $\left. \left\{ x , \frac { x } { 2 } - 4 \right\} \right\}$
D) $\left\{ \left\{ x , 4 - \frac { x } { 2 } \right) \right\}$

Question

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l } 
x - 2 y = 8 \
- 3 x + 6 y = - 24
\end{array}$$
A) $\varnothing$
B) $\left. \left\{ x , \frac { x } { 6 } - 4 \right\} \right\}$
C) $\left. \left\{ x , \frac { x } { 2 } - 4 \right\} \right\}$
D) $\left\{ \left\{ x , 4 - \frac { x } { 2 } \right) \right\}$

Quizplus · Accepted Answer

The second equation is a multiple of the first, indicating the lines are coincident, leading to infinitely many solutions. Solving the first equation for $y$ gives $y = \frac{x}{2} - 4$, matching choice C.

Solve the System x−2y=8−3x+6y=−24\begin{array} { l } x - 2 y = 8 \\- 3 x + 6 y = - 24\end{array}x−2y=8−3x+6y=−24​

Solve the System $\begin{array} { l } x - 2 y = 8 \\- 3 x + 6 y = - 24\end{array}$