Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l }
x - 8 y = 2 \
- 3 x + 24 y = - 6
\end{array}$$
A) $\varnothing$
B) $\left\{ \left\{ x , \frac { x } { 8 } - \frac { 1 } { 4 } \right) \right\}$
C) $\left\{ \left\{ x , \frac { x } { 24 } - \frac { 1 } { 4 } \right) \right\}$
D) $\left\{ \left( x , \frac { 1 } { 4 } - \frac { x } { 8 } \right) \right\}$

Question

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l } 
x - 8 y = 2 \
- 3 x + 24 y = - 6
\end{array}$$
A) $\varnothing$
B) $\left\{ \left\{ x , \frac { x } { 8 } - \frac { 1 } { 4 } \right) \right\}$
C) $\left\{ \left\{ x , \frac { x } { 24 } - \frac { 1 } { 4 } \right) \right\}$
D) $\left\{ \left( x , \frac { 1 } { 4 } - \frac { x } { 8 } \right) \right\}$

Quizplus · Accepted Answer

The second equation is a multiple of the first, indicating the system has infinitely many solutions. The solution set can be expressed with $x$ arbitrary, and solving the first equation for $y$ gives $y = \frac{x}{8} - \frac{1}{4}$.

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

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