Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { l }
3 x = y + 3 \
6 x - 2 y = 3
\end{array}$$
A) Inconsistent and dependent
B) Consistent and independent
C) Inconsistent and independent
D) Consistent and dependent

Question

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { l } 
3 x = y + 3 \
6 x - 2 y = 3
\end{array}$$
A) Inconsistent and dependent
B) Consistent and independent
C) Inconsistent and independent
D) Consistent and dependent

Quizplus · Accepted Answer

We can solve for y in terms of x from the first equation: $y=3x-3$.
Substituting this into the second equation, we get $6x-2(3x-3) = 3$, which simplifies to $0=9$.
Since this is a contradiction, the system is inconsistent. Also, since there are infinitely many values of $x$ that do not satisfy the system, the system is independent. Therefore, the correct choice is (C).

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