Answer
Inconsistent
Work Step by Step
Simplify each equation to slope-intercept form by isolating $y$ on the left side:
$6y=-2x+8
\\\frac{6y}{6}=\frac{-2x+8}{6}
\\y=-\frac{1}{3}x+\frac{8}{6}
\\y=-\frac{1}{3}x + \frac{4}{3}$
Other equation:
$12y=-4x+4
\\\frac{12y}{12}=\frac{-4x+4}{12}
\\y=-\frac{1}{3}x +\frac{1}{3}$
The lines have same slope but different y-intercepts.
Thus, they are distinct parallel lines making the system inconsistent.
