Question

What type of system is the following set of equations?

{-3x + y = -2
y - 4 = -6x

a. consistent, independent
b. consistent, dependent
c. inconsistent
d. independent

Answer 1

`-3x+y=-2 \\ y-4=-6x \ \ \ |* (-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=(-6)/(-9) \\ x=(2)/(3) \\ \\ y-4=-6 * (2)/(3) \\ y-4=-4 \\ y=-4+4 \\ y=0 \\ \\ (x,y)=((2)/(3),0)`

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