Question

What type of system is the following set of equations?

Answer 1

$-3x+y=-2 \\ y-4=-6x \ \ \ |\times (-1) \\ \\ -3x+y=-2 \\ \underline{-y+4=6x} \\ -3x+y-y+4=6x-2 \\ -3x+4=6x-2 \\ -3x-6x=-2-4 \\ -9x=-6 \\ x=\frac{-6}{-9} \\ x=\frac{2}{3} \\ \\ y-4=-6 \times \frac{2}{3} \\ y-4=-4 \\ y=-4+4 \\ y=0 \\ \\ (x,y)=(\frac{2}{3},0)$

The system has one solution so it's A. consistent and independent.