Write the word or phrase that best completes each statement or answers the question.
-$$\begin{array} { l }
y = 6 x + 30 \
9 x + 8 y = - 102
\end{array}$$
A) Dependent, $( x , 6 x + 30 )$
B) $( 6,6 )$
C) Inconsistent, Ø
D) $( - 6 , - 6 )$

Question

Write the word or phrase that best completes each statement or answers the question.
-$$\begin{array} { l } 
y = 6 x + 30 \
9 x + 8 y = - 102
\end{array}$$
A) Dependent, $( x , 6 x + 30 )$
B) $( 6,6 )$
C) Inconsistent, Ø
D) $( - 6 , - 6 )$

Quizplus · Accepted Answer

To solve the system, we could substitute y = 6x + 30 into the second equation and get 9x + 8(6x + 30) = -102, which simplifies to 57x = -390. Solving for x, we get x = -6. Then, using either equation, we can solve for y and find that y = -6. Therefore, the solution to the system is ( -6, -6), which corresponds to choice D. The system is consistent and independent, with a unique solution.

Write the Word or Phrase That Best Completes Each Statement y=6x+309x+8y=−102\begin{array} { l } y = 6 x + 30 \\9 x + 8 y = - 102\end{array}y=6x+309x+8y=−102​

Write the Word or Phrase That Best Completes Each Statement $\begin{array} { l } y = 6 x + 30 \\9 x + 8 y = - 102\end{array}$