Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l }
3 x - y - 2 = 0 \
- 6 x + 2 y + 4 = 0
\end{array}$$
A) $\varnothing$
B) $\{ ( x , 3 x - 2 ) \}$
C) $\{ ( x , 6 x - 2 ) \}$
D) $\{ ( x , 2 - 3 x ) \}$

Question

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.
-$$\begin{array} { l } 
3 x - y - 2 = 0 \
- 6 x + 2 y + 4 = 0
\end{array}$$
A) $\varnothing$
B) $\{ ( x , 3 x - 2 ) \}$
C) $\{ ( x , 6 x - 2 ) \}$
D) $\{ ( x , 2 - 3 x ) \}$

Quizplus · Accepted Answer

The second equation is exactly -2 times the first equation, indicating that they are dependent and represent the same line. Therefore, there are infinitely many solutions, and the solution set can be expressed with $x$ arbitrary and $y$ in terms of $x$ as $y = 3x - 2$.

Solve the System 3x−y−2=0−6x+2y+4=0\begin{array} { l } 3 x - y - 2 = 0 \\- 6 x + 2 y + 4 = 0\end{array}3x−y−2=0−6x+2y+4=0​

Solve the System $\begin{array} { l } 3 x - y - 2 = 0 \\- 6 x + 2 y + 4 = 0\end{array}$