Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { r r }
3 x - 3 y + 6 z = & - 30 \
- 15 x + 15 y - 30 z = & 150 \
12 x - 12 y + 24 z = & - 120
\end{array} \right.$$
A) $\{ ( 4 , - 9 , - 4 ) \}$
B) $\{ ( 4 , - 4 , - 9 ) \}$
C) infinitely many solutions; dependent equations
D) no solution or $\varnothing$

Question

Solve the system. If there is no solution or if the system's equations are dependent, so state.
-$$\left\{ \begin{array} { r r } 
3 x - 3 y + 6 z = & - 30 \
- 15 x + 15 y - 30 z = & 150 \
12 x - 12 y + 24 z = & - 120
\end{array} \right.$$
A) $\{ ( 4 , - 9 , - 4 ) \}$
B) $\{ ( 4 , - 4 , - 9 ) \}$
C) infinitely many solutions; dependent equations
D) no solution or $\varnothing$

Quizplus · Accepted Answer

The given system of equations is dependent. Each equation is a multiple of the others (the second equation is -5 times the first, and the third is 4 times the first), which means they represent the same plane in three-dimensional space, leading to infinitely many solutions.

Solve the System {3x−3y+6z=−30−15x+15y−30z=15012x−12y+24z=−120\left\{ \begin{array} { r r } 3 x - 3 y + 6 z = & - 30 \\- 15 x + 15 y - 30 z = & 150 \\12 x - 12 y + 24 z = & - 120\end{array} \right.⎩⎨⎧​3x−3y+6z=−15x+15y−30z=12x−12y+24z=​−30150−120​

Solve the System $\left\{ \begin{array} { r r } 3 x - 3 y + 6 z = & - 30 \\- 15 x + 15 y - 30 z = & 150 \\12 x - 12 y + 24 z = & - 120\end{array} \right.$