Decide whether the system $\left\{ \begin{array} { c }
3 x - 6 y = 6 \
- 12 x + 24 y = - 24
\end{array} \right.$ is consistent or inconsistent.
A)inconsistent
B)consistent

Question

Decide whether the system $\left\{ \begin{array} { c } 
3 x - 6 y = 6 \
- 12 x + 24 y = - 24
\end{array} \right.$ is consistent or inconsistent.
A)inconsistent
B)consistent

Quizplus · Accepted Answer

This system is consistent because the second equation is just the first equation multiplied by -4. Therefore, the two equations are really just stating the same thing and are not independent. This means that the system has infinitely many solutions, which makes it consistent.

Decide Whether the System {3x−6y=6−12x+24y=−24\left\{ \begin{array} { c } 3 x - 6 y = 6 \\- 12 x + 24 y = - 24\end{array} \right.{3x−6y=6−12x+24y=−24​

Decide Whether the System $\left\{ \begin{array} { c } 3 x - 6 y = 6 \\- 12 x + 24 y = - 24\end{array} \right.$