Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { c }
- 10 x - 2 y = 10 \
5 x - y = - 5
\end{array}$$
A) Consistent and independent
B) Inconsistent and independent
C) Inconsistent and dependent
D) Consistent and dependent

Question

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { c } 
- 10 x - 2 y = 10 \
5 x - y = - 5
\end{array}$$
A) Consistent and independent
B) Inconsistent and independent
C) Inconsistent and dependent
D) Consistent and dependent

Quizplus · Accepted Answer

The system is consistent because there is at least one solution, and it is independent because it has exactly one solution. Multiplying the second equation by 2 gives -10x - 2y = 10, which is a multiple of the first equation, indicating they are two distinct lines that intersect at one point.

Classify the System as Consistent or Inconsistent, and Dependent or Independent