Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { c }
x + 6 y = 17 \
2 x + 12 y = 34
\end{array}$$
A) Inconsistent and dependent
B) Consistent and dependent
C) Inconsistent and independent
D) Consistent and independent

Question

Classify the system as consistent or inconsistent, and dependent or independent.
-$$\begin{array} { c } 
x + 6 y = 17 \
2 x + 12 y = 34
\end{array}$$
A) Inconsistent and dependent
B) Consistent and dependent
C) Inconsistent and independent
D) Consistent and independent

Quizplus · Accepted Answer

We can rearrange the equations to be in slope-intercept form: 
$$y = -\frac{1}{6}x +\frac{17}{6}$$ 
$$y = -\frac{1}{6}x + \frac{17}{6}$$ 
Both equations have the same slope and y-intercept, meaning that they describe the same line. Therefore, the equations are dependent. To check for consistency, we can substitute the second equation into the first and simplify: 
$$x + 6\left(-\frac{1}{6}x + \frac{17}{6}\right) = 17$$ 
$$x - x + 17 = 17$$ 
The equation is true, so the system is consistent. Therefore, the answer is B: Consistent and dependent.

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